Inverse Functions Review

Inverse Relations & Functions Review

​Dr. Tom Giles

​4 steps to find inverse function

•Step1: Let f(x) = y

•Step 2: Interchange x and y

•Step 3: Solve for y

•Step 4: Change y to f^-1(x)

Subject | Subject

Some text here about the topic of discussion

​Find the inverse of the following function: f(x) = x -3

​4 steps to find inverse function

•Step1: Let f(x) = y

•Step 2: Interchange x and y

•Step 3: Solve for y

•Step 4: Change y to f^-1(x)

Subject | Subject

Some text here about the topic of discussion

​Find the inverse of the following function: f(x) = x -3

Multiple Choice

Find the inverse of f(x) = -4x - 12

• f^-1(x) = 4x - 3
• f^-1(x) = -1/4x - 3
• f^-1(x) = 1/4x + 3
• f^-1(x) = -4x - 3

Multiple Choice

Are the following inverses of each other? Use composition of functions. fog(x) and gof(x)

• True

• False

Multiple Choice

Was the inverse function found correctly?

• no,
• yes

Multiple Choice

Find the inverse of
f(x) = 1/4x - 7

• f^-1(x) = 4x + 7
• f^-1(x) = -4x + 28
• f^-1(x) = -4x - 7
• f^-1(x) = 4x + 28

Multiple Choice

Find the inverse of the function
f(x) = 3x − 5

• f^-1(x)=3x +5
• f^-1(x)=(x+5)/3
• f^-1(x)=3y-5
• f^-1(x)=3y+5

Multiple Choice

What does it mean to find the inverse of a function?

• the x's and y's are switched
• the x's and y's are divided by 2
• the x's and y's are made negative
• the x's and y's are the same

Multiple Choice

If f(x)=x+5, what is f^-1(x)?

• (x + 5)²

• x - 5

• (x + 5)^-1

• undefined

Multiple Choice

If f(x)=3x, what is f^-1(x)?

• x/3

• 3x²

• 3x + 3x

• 3x^-1

Multiple Choice

f(x) = 3x + 10

g(x) = ⅓x - 3

Find g(f(x))

• f(g(x)) = 1

• f(g(x)) = x

• f(g(x)) = 0

• None of these.

Multiple Choice

What is the inverse of the function
f(x) = 2x + 4   ?

• f^-1(x) = 4(x -2)
• f^-1(x) = (x-4)/2
• f^-1(x) = x/2 - 4
• f^-1(x) = x/4 + 2

Multiple Choice

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

• (1, 4) and (4, 6)
• (-4, -1) and (-6, -4)
• (-1, -4) and (-4, -6)
• (4, 1) and (6, 4)

Multiple Choice

What is the inverse of the points
(1,3)(2,4)(6,8)

• (3,1)(4,2)(8,6)
• (-3,-1)(-4,-2)(-8,-6)
• (1,3)(2,4)(6,8)
• (-1,-3)(-2,-4)(-6,-8)

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• 9

• 3

• 5

• √15

Multiple Choice

• 9 - √17

• 4

• 2

• √8

Multiple Choice

• -1
• 1
• -1/3
• -5/3

Multiple Choice

When f(x) = x²-3 and g(x) = 2x+8 , find g(f(2)).

• 14
• 10
• 144
• 141

Multiple Choice

Find the inverse function

• a

• b

• c

• d

Multiple Choice

Which graph is the inverse of the function f(x) = 3x+1?

• a

• b

• c

• d

Multiple Choice

Which graph could represent both a function (blue) and its inverse (red) graphed on the

same coordinate grid?

• a

• b

• c

• d

Multiple Choice

Graph the relation with closed circles and its inverse with open circles.

Then select the graph that depicts that layout.

• a

• b

• c

• d

Multiple Choice

Is g(x) an Inverse Function of f(x)?

• Inverse Functions

• Not Inverse Functions

Multiple Choice

Is g(x) an Inverse Function of f(x)?

• Inverse Functions

• Not Inverse Functions

Multiple Choice

Is g(x) an Inverse Function of f(x)?

• Inverse Functions

• Not Inverse Functions

Multiple Choice

Is g(x) an Inverse Function of f(x)?

• Inverse Functions
• Not Inverse Functions

Multiple Choice

What does an inverse function do?

• Nothing

• Makes it bigger

• Does the opposite of the original function

Multiple Choice

What is the inverse of this function?

• A
• B
• C
• D