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?

Back

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

Front

If f(x) = x + 5, what is f⁻¹(x)?

Back

f⁻¹(x) = x - 5.

Front

If f(x) = 3x - 5, what is f⁻¹(x)?

Back

f⁻¹(x) = (x + 5)/3.

Front

If f(x) = 2x + 4, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 4)/2.

Front

If f(x) = 4 - 2x, what is f⁻¹(x)?

Back

f⁻¹(x) = 2 - ½x.

Front

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

Back

Replace f(x) with y.

Front

What do you do after switching x's and y's when finding an inverse?

Back

Solve for y.

Front

What is the notation for an inverse function?

Back

f⁻¹(x) denotes the inverse of the function f(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.