Inverse Functions Notes Review

Front

How can you find the inverse of a function algebraically?

Back

Replace f(x) with y, swap x and y, then solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What happens when you reflect a point over the line y = x?

Back

The x-coordinate and y-coordinate swap places.

Front

Which of the following statements is true about the horizontal line test?

Back

It determines if a function is one-to-one.

Front

What is the inverse of the function f(x) = 3x + 6?

Back

f^(-1)(x) = (1/3)x - 2.

Tags

CCSS.HSF-BF.B.4A

Front

What is the inverse of the function g(x) = (1/3)x - 2?

Back

g^(-1)(x) = 3x + 6.

Tags

CCSS.HSF-BF.B.4A

Front

Define an inverse function.

Back

An inverse function reverses the operation of the original function.

Tags

CCSS.HSF-BF.B.4A

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

What is the condition for a function to have an inverse?

Back

A function must be one-to-one (bijective) to have an inverse.

Tags

CCSS.HSF-BF.B.4D

Front

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

Back

If f(g(x)) = x and g(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

What is the inverse of the function f(x) = x^2 (for x >= 0)?

Back

f^(-1)(x) = √x.

Tags

CCSS.HSF-BF.B.4D