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. The resulting equation is the inverse function.

Front

What is the inverse of f(x) = -4x - 12?

Back

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

Front

What is the inverse of f(x) = 4x?

Back

f^-1(x) = \frac{x}{4}.

Front

What is the inverse of f(x) = x⁴ - 2?

Back

f^-1(x) = ∜(x + 2).

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

Back

f^-1(b) = a.

Front

What is the inverse of f(x) = 3x + 15?

Back

f^-1(x) = \frac{x - 15}{3}.

Front

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

Back

Replace f(x) with y.