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

To find the inverse of a function, replace f(x) with y, swap x and y, and then solve for y.

Front

Find the inverse of f(x) = -4x - 12.

Back

f^-1(x) = -1/4x - 3.

Front

Find the inverse of f(x) = 1/4x - 7.

Back

f^-1(x) = 4x + 28.

Front

Find the inverse of f(x) = 3x - 5.

Back

f^-1(x) = (x + 5)/3.

Front

What is the notation for an inverse function?

Back

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

Front

If f(a) = b, what is f^-1(b)?

Back

f^-1(b) = a.

Front

What is the graphical representation of an inverse function?

Back

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

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse undo each other. For example, f(f^-1(x)) = x and f^-1(f(x)) = x.

Front

Find f^-1(-2) given f(x) = x + 3.

Back

f^-1(-2) = -5.