Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function, switching the roles of inputs and outputs.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, switch x and y, and solve for y.

Front

What is the inverse of f(x) = 3x - 5?

Back

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

Front

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

Back

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

Front

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

Back

It means to switch the x's and y's in the function.

Front

What is the notation for an inverse function?

Back

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

Front

If g(x) = ⅓x - 3, what is g(f(x))?

Back

g(f(x)) = None of these.

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

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

Back

Replace f(x) with y.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse if it is one-to-one.