Intro to Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^-1(y) takes y back to x.

Tags

CCSS.HSF-BF.B.4A

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Switch x and y. 3. Solve for y. 4. Replace y with f^-1(x).

Tags

CCSS.HSF-BF.B.4A

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f^-1(x).

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are reflections of each other across the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

If f(x) = 2x + 3, what is f^-1(x)?

Back

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

Tags

CCSS.HSF-BF.B.4A

Front

What does it mean for two functions to be inverses of each other?

Back

If f(g(x)) = x and g(f(x)) = x for all x in the domain, then f and g are inverse functions.

Tags

CCSS.HSF-BF.B.4B

Front

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

Back

Replace f(x) with y.

Tags

CCSS.HSF-BF.B.4A

Front

True or False: To find the inverse of a function, you must switch the x's and y's after replacing f(x) with y.

Back

TRUE.

Tags

CCSS.HSF-BF.B.4A

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is obtained by reflecting the graph of the original function across the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

If f(x) = x², does it have an inverse?

Back

No, f(x) = x² does not have an inverse because it is not one-to-one.