Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect 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, swap the x and y in the equation and solve for y.

Front

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

Back

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

Front

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

Back

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

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

What operation allows us to verify if functions are inverses?

Back

Composing the functions. If f(f^-1(x)) = x and f^-1(f(x)) = x, then they are inverses.

Front

What is the inverse of a linear function?

Back

The inverse of a linear function is also a linear function, provided the original function is one-to-one.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning it passes the horizontal line test.

Front

If f(x) = ax + b, what is the general form of its inverse?

Back

The inverse is f^-1(x) = (x - b)/a.