Understanding Inverse Functions

What is the first step in finding the inverse of a function?

• Switch x and y

• Replace f(x) with y

• Graph the function

• Solve for x

Tags

CCSS.HSF-BF.B.4A

What is the inverse function of f(x) = 3x + 9?

• y = (x - 9) / 3

• y = 3x - 9

• x = (y - 9) / 3

• x = 3y + 9

Tags

CCSS.HSF-BF.B.4A

When finding the inverse of a quadratic function, why do we add plus or minus after taking the square root?

• To account for both positive and negative roots

• To simplify the equation

• To make the function invertible

• Because the original function is quadratic

Tags

CCSS.HSF-BF.B.4D

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

• y = ±sqrt(x + 4)

• y = sqrt(x - 4)

• y = sqrt(x) - 4

• y = sqrt(x + 4)

Tags

CCSS.HSF-BF.B.4A

What is the inverse function of f(x) = the cube root of (3x + 8)?

• y = x^3 + 8

• y = 3x + 8

• y = (x^3 - 8) / 3

• y = 3x^3 + 8

Tags

CCSS.HSF-BF.B.4A

How do you verify if two functions are inverses of each other?

• By graphing them

• By solving f(g(x)) = x and g(f(x)) = x

• By finding their derivatives

• By checking if they have the same domain and range

Tags

CCSS.HSF-BF.B.4B

What does the horizontal line test determine?

• If a function is increasing or decreasing

• If a function is one-to-one

• If a function is continuous

• If a function has an inverse that is also a function

What property do inverse functions have in relation to the line y = x?

• They intersect at y = x

• They are symmetric about y = x

• They are parallel to y = x

• They are identical to y = x

Tags

CCSS.HSF-BF.B.4C

If a function fails the horizontal line test, what does it imply about its inverse?

• The inverse is a linear function

• The inverse is a quadratic function

• The inverse is not a function

• The inverse is also a function

What is the inverse function of f(x) = x^2, considering only the right side of the graph?

• y = sqrt(x)

• y = x/2

• y = ±sqrt(x)

• y = x^2

Tags

CCSS.HSF-BF.B.4D