Inverse Functions Review #2

Front

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

Back

The x's and y's are switched.

Front

How can you determine if two functions are inverses?

Back

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

Front

The inverse of the function f(x) is written as ...

Back

f^{-1}(x)

Front

What is the graphical representation of inverse functions?

Back

They are reflected over the line y = x.

Front

What is the domain of the inverse function?

Back

It is the range of the original function.

Front

What is the range of the inverse function?

Back

It is the domain of the original function.

Front

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

Back

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

Front

What happens to the x-intercept of a function when finding its inverse?

Back

The x-intercept becomes the y-intercept of the inverse function.

Front

What is a one-to-one function?

Back

A function where each output is produced by exactly one input.

Front

Can a function have an inverse if it is not one-to-one?

Back

No, only one-to-one functions have inverses.