Based on the graph given for f (x) construct the graph of f¹ (x). for f (x) find E, F and the formula of f (x) when it is known that it is a linear function.
Answers
Answer:
To find an inverse function, reflect a graph of a function across the line y=x (and find the resulting equation)
To reflect a linear function in the line y=x, find points on f(x) and then swap their x and y coordinates.
Points on f(x): (0, -4) (2, 0) (5, 6)
Points reflected in line y=x: (-4, 0) (0, 2) (6, 5)
Plot points (-4, 0) (0, 2) (6, 5) and connect to form a straight line - this is the inverse of the function: [tex]f^{-1}(x)[/tex]
To determine the equation of f(x):
Choose 2 points on f(x): (5, 6) and (0, -4)
Calculate the slope (gradient) by using:
[tex]m=\dfrac{\triangle y}{\triangle x}=\dfrac{y_2-y_1}{x_2-x_1}=\frac{6--4}{5-0}=2[/tex]
Using the slope-intercept form: y = mx + b
(where m is the slope and b is in the y-intercept)
From inspection of the graph, we can see the line crosses the y-axis at -4,
⇒ f(x) = 2x - 4
As the line is actually a line segment (with endpoints (0, -4) and (5, 6), then
f(x) = 2x - 4, 0 ≤ x ≤ 5
To determine the equation of [tex]f^{-1}(x)[/tex]:
Rewrite f(x) as [tex]y = 2x - 4[/tex]
Swap the x and y: [tex]x = 2y - 4[/tex]
Rearrange to make y the subject: [tex]y= \dfrac{1}{2}(x + 4)[/tex]
Replace y with [tex]f^{-1}(x)[/tex]
So the equation of the inverse is: [tex]f^{-1}(x)= \dfrac{1}{2}(x + 4)[/tex]
As the original function is a segment, then
[tex]f^{-1}(x)= \dfrac{1}{2}(x + 4), \ \ \ -4\leq x\leq 6[/tex]
(shown in blue on the attached diagram)
** I can't see any points labelled E and F on the original function. If they are the endpoints of the line segment of f(x), then they are (0, -4) and (5, 6) **
Related Questions
A random sample of 24 corporate-owned stores finds an average number of customers of 313 with a standard deviation of 34.9. What is the upper bound of a 95% confidence interval for the average number of customers in corporate-owned stores
Answers
Answer:
95% is 1700 customers
Step-by-step explanation:
JK i actually dont know but thnks for the points BTW
If f(x)= x^2-25 and g(x)=x-5, what is the domain of (f/g)(x)?
Answers
Answer:
B) all real values of x except x=5
Step-by-step explanation:
If [tex]f(x)=x^2-25[/tex] and [tex]g(x)=x-5[/tex], then [tex]\bigr(\frac{f}{g}\bigr)(x)=\frac{f(x)}{g(x)}=\frac{x^2-25}{x-5}=\frac{(x-5)(x+5)}{(x-5)}[/tex].
Given that [tex]x-5[/tex] exists in both the numerator and denominator, this creates a hole on the graph of the function where [tex]x=5[/tex] since [tex]5-5=0[/tex]all real values of x except x=5 is correct.
Review the attached graph for more information
How do I do this? Please help!
Answers
I already answered this question, if you look back in your questions you should find this answered along with another one. I'll do it again just in case you don't find it.
Answer:
{y,x} = {-4,-2}
Expanation:
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = 2x
// Plug this in for variable y in equation [2]
[2] -2•(2x) - 8x = 24
[2] - 12x = 24
// Solve equation [2] for the variable x
[2] 12x = - 24
[2] x = - 2
// By now we know this much :
y = 2x
x = -2
// Use the x value to solve for y
y = 2(-2) = -4
please help!! Tysm <33
Answers
Answer:
[tex] \frac{p}{3} = 5[/tex]
p = 15
[tex] \frac{15}{3} = 5[/tex]
!!!HURRY PLS!!!
My BraIns nOt wOrkIng-
Answers
Answer:
x=5
Step-by-step explanation:
x+3=2x-2
1. take the square root's out
2. subtract -3 from both sides of the equation.
x+3-3=2x-2-3
3. subtract.
x=2x-5
4. subtract 2x from both sides of the equation.
x=-2x=2x-5-2x
5. solve
x=5
Hey would really appreciate the help!
Answers
Answer:
a. (2c+1b)-1w
b. monomial
Step-by-step explanation:
helpp pleacee??!!!!!
Answers
Answer:
9
Step-by-step explanation:
I need to write 20 characters
9. Which set of ratios below is NOT equivalent
to 3:4?
the
bu
A. 6 to 9,
q
12
B.) 9 to 12, 20
15
Answers
Answer:
A
Step-by-step explanation: {reduction}
{[tex]\frac{2X3}{3X3}=\frac{2}{3}[/tex]} {[tex]\frac{3X3}{3X4}=\frac{3}{4}[/tex]}
A. 6 to 9 7'5 [tex]\frac{6}{9}=\frac{2}{3} , \frac{9}{12}=\frac{3}{4}[/tex]
{[tex]\frac{3X3}{3X4}=\frac{3}{4}[/tex]}
B. 9 to 12 7'5 [tex]\frac{9}{12}=\frac{3}{4} , \frac{15}{20}=\frac{3X5}{4X5}=\frac{3}{4}[/tex]
C. [tex]\frac{15}{20}=\frac{3}{4} ,[/tex] 24 = 32 = 3 × 8: 4 ×8 = 3 = 4
D. [tex]\frac{30}{40}=\frac{3X10}{4X10}=\frac{3}{4} , 18:24=3X6=4X6=3:4[/tex]
choose A
Math asap!! Will give brainliest
Answers
Step-by-step explanation:
line QS = RS
line KJ = half of line KC
WHAT IS THE VOLUME OF THE PRISM????
Answers
Answer:
78 3/4
Step-by-step explanation:
Convert all the mixed numbers to fraction : 4 1/2 = 9/2 ; 3 1/2 = 7/2
V = 9/2 x 5 x 7/2 = 315 / 4 = 78 3/4
Hope it helps
In the figure above, the measure of <BDE is 20 and CD is perpendicular to DE. What is the measure of <ADC ?
Answers
Answer:
∠ ADC = 110°
Step-by-step explanation:
∠ CDE = 90° ( angle between perpendicular lines ) , then
∠ CDB + ∠ BDE = 90°
∠ CDB + 20° = 90° ( subtract 20° from both sides )
∠ CDB = 70°
∠ ADC and ∠ CDB are adjacent angles on a straight line and sum to 180° , so
∠ ADC + ∠ CDB = 180° , that is
∠ ADC + 70° = 180° ( subtract 70° from both sides )
∠ ADC = 110°
the Nth term of a geometric sequence is given by this equation, solve it and show ALL of your steps. 4 through 7
Answers
Answer:
I dont know the answers but here is an example( look at screenshots)
Step-by-step explanation:
8x3+26x2+19x+3 is divided by 4x+3
Answers
Answer:
Remainder=35.25
Quotient = 2x²+8x+10.7
.i need help w this pls!!
Answers
——. Tried to make it look like a
y Fraction
If you can’t read it like that then x-y / y
For simplifying this fraction, let first consider it as
[tex]{:\implies \quad \sf \dfrac{x}{y}-1}[/tex]
If we take LCM, and simplify it further, we will be having ;
[tex]{:\implies \quad \sf \dfrac{x\cdot 1-1\cdot y}{y}}[/tex]
[tex]{:\implies \quad \boxed{\bf{\dfrac{x-y}{y}}}}[/tex]
This is the required answer
Solve the equation below pls show your work no links pls.
[tex](9^{2} )^{-1/3}[/tex]
Answers
Given :-
[tex](9^{2} )^{-1/3}[/tex]To Find :-
To solve the expression .Solution :-
Given expression to us is ,
[tex](9^{2} )^{-1/3}[/tex]
We know that ,
[tex] 9 = 3^2[/tex]
So our expression becomes ,
[tex]\{ (3^2)^2\}^{\frac{-1}{3}}[/tex]
And , [tex] (a^m)^n =a^{mn}[/tex] . Using this ,
[tex] (3^4)^{\frac{-1}{3}}[/tex]
Again using the same law ,
[tex] 3^{\frac{-4}{3}}[/tex]
We know that , [tex] a^{-m}=\frac{1}{a^m}[/tex] . Therefore ,
[tex] (3^{-4})^{\frac{1}{3}}[/tex]
[tex]\\\bigg( \dfrac{1}{3^4}\bigg)^{1/3}[/tex]
[tex]\\ \dfrac{1}{\sqrt[3]{3^4}}[/tex]
Simplify ,
[tex] \dfrac{1}{3\sqrt[3]{3}}[/tex]
This is the simplified expression.
I hope this helps.
y=28(0.25)^x WHAT IS THE FREAKING PERCENT? Thank you! <3?
Answers
Answer:
75%
Step-by-step explanation:
Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
248 legs. Assuming there are no mutations in the animals, determine exactly how many ducks and cows he saw. Let
X represent the number of ducks and y represent the cows.
Total Equation:
Legs Equation:
How many ducks?
How many cows?
Answers
Answers:
Total equation: x+y = 80Legs equation: 2x+4y = 248How many ducks? 36How many cows? 44====================================================
Further explanation:
x = number of ducksy = number of cowsx+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
2x = number of legs from all the ducks only4y = number of legs from all the cows only2x+4y = total number of legs from both types of animals combinedWe're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
------------
Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
------------
Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
Choose the correct product of (7x − 6)2. 49x2 84x 36 49x2 − 36 49x2 36 49x2 − 84x 36.
Answers
Answer:
the answer for this question is 49x²-84x+36
hope it helps
Answer:49x²-84x+36
Step-by-step explanation:
True
Consider the equation q = 4 +0.8p.
=
What value of p would make the equation to
12?
Answers
Answer:
p=10
Step-by-step explanation:
q = 4 +0.8p
Let q = 12
12 = 4 +0.8p
Subtract 4 from each side
12-4 = 4+.8p -4
8 = .8p
Divide each side by .8
8/.8 = .8p/.8
10 =p
HELP MY GRADE 9 PLS AND THANK YOU
Answers
Answer:
64x²y²
Step-by-step explanation:
Use the great smart calculator
hope it helpz uuuuuuu
Two fair 6 sided number cubes are rolled. What is the probability of rolling a sum of 11?
Question 3 options:
1/6
1/36
1/18
11/36
Answers
There are two ways to make a sum of 11: 5,6 or 6,5. This means that the probability is 2/36 which equals 1/18.
The points F(4,
-2), G(9,
-6), H (8, -1), and I (5, 2) form a quadrilateral. Find
the desired slopes and lengths, then fill in the words that BEST identifies the type of
quadrilateral.
(PICTURE BELOW)
Answers
slope of GH
and
lenght of FG
What is the volume of this sphere? Use 3. 14 for pi and round to the nearest hundredth when necessary. 50. 24 m³ 267. 95 m³ 1607. 68 m³ 2143. 57 m³.
Answers
Volume of a figure is the measurement of space occupied by the figure. The volume of the specified sphere is given by Option B: 267. 95 m³
What is the volume of sphere?If the given sphere is of radius r units, then its volume is given as:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]
For the given sphere, its diameter is 8 units, thus, its radius is half of its diameter and thus, of 4 units.
Thus, volume of specified sphere is obtained as:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3\\\\V = \dfrac{4}{3} \pi (4)^3 =\dfrac{256}{3} \times 3.14 \approx 267.95 \: m^3[/tex]
Thus,
Volume of a figure is the measurement of space occupied by the figure. The volume of the specified sphere is given by Option B: 267. 95 m³
Learn more about volume of sphere here:
https://brainly.com/question/381274
What is the surface area of this triangular prism rounded to the nearest tenth?
Answers
The surface area of the triangular prism, rounded to the nearest tenth is: 85.7 cm²
What is the Surface Area of a Triangular Prism?Surface area (SA) = bh + (s1 + s2 + s3)H
Given:
s1 = 6.8 cm
s2 = 5.1 cm
s3 = 8.5 cm
H = 2.5 cm
b = 6.8 cm
h = 5.1 cm
Plug in the values
Surface area of the triangular prism = 6.8 × 5.1 + (6.8 + 5.1 + 8.5)2.5
Surface area of the triangular prism = 85.7 cm²
Learn more about the surface area of a triangular prism on:
https://brainly.com/question/16147227
8 and 9 plus explanation pls
Answers
Answer:
42
Step-by-step explanation:
A small school employs 5 teachers who make between $40,000,and 70,000 per year.
The newest teacher, Valerie, decides to teach part-time which decreases her salary from 40,000 to 20,000 per year. The rest of the salaries stay the same.
How will decreasing Valerie's salary affect the mean and median?
HELP PLEASE
Answers
Answer:
Its B
Step-by-step explanation:
No of teachers in the school = 5
Salaries they make =40000 to 70000
When one of the five teachers reduce salary to 20000/- per year, median may or may not shift one number to the left
Mean will definitely decrease by difference/5 = 4000 dollars
Thus mean will defintely change by reduction of 4000 dollars.
Median has a chance to remain the same or may shift left side one item.
Which value of x makes the equation 0.1x – 2.5 = 1.0 true?
a. 10
b. 15
c. 20
d. 35
Answers
Answer:
d) 35
Step-by-step explanation:
0,1 *35 - 2,5 = 1,0
what is 4.09 less than 5.6 ??
Answers
Answer: -1.51, or it could be 4.09 < 5.6 (Im sorry if I get it wrong I just wanted to help)
Step-by-step explanation:
The value of the subtraction is 1.51.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given numbers are 4.09 and 5.6. The value of 4.09 less than 5.6 will be calculated as:-
Subtraction = 5.6 - 4.09
Subtraction = 1.51
Therefore, the value of the subtraction is 1.51.
To know more about an expression follow
https://brainly.com/question/25421984
#SPJ2
In basketball, some baskets are worth two points. Others are worth three points. In one game, the ratio of three-point baskets to three-point tries for one team was 3 : 4. If the team scored 27 points from three-point baskets, how many three-point tries did the team have?
Answers
Answer:
Writing the information in the form of ratio
Three point basket = Three point tries
3 : 4
27 : x
Think about multiplication , how many 3s do you need to make 27 ?
Its 27 ÷ 3= 9
Because you need 9 lots of 3, Then to make it proportional , you'd need 9 lots of 4
9×4 = 36
Three points tries is 36
A square has a perimeter of 39.6 millimeters. What is the length of each side?
Answers
Answer:
9.9 millimeters
Step-by-step explanation:
To find the perimeter of a square,
Equation: 4 • length = P
So in this case, we're just working backwards. To find the length, divide.
39.6/4 = 9.9
Answer:
9.9 mm
Step-by-step explanation:
let [tex]x[/tex] = length of one edge of the square
perimeter of a square = 4[tex]x[/tex]
⇒ 39.6 = 4[tex]x[/tex]
⇒ [tex]x[/tex] = 39.6 ÷ 4 = 9.9 mm