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.

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).

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.

Front

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

Back

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

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.

Front

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

Back

Replace f(x) with y.

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.

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.

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.