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 does it mean for a function to be invertible?

Back

A function is invertible if it has a unique output for every input, meaning it passes the horizontal line test.

Front

Given the coordinates (1, 2), what is the inverse?

Back

(2, 1).

Front

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

Back

f^-1(b) = a.

Front

What is the inverse of the function f(x) = x²?

Back

The inverse is not a function because it fails the horizontal line test. However, the square root function g(x) = √x is often considered the 'inverse' for non-negative x.

Front

How do you determine f^-1(2) given f(1) = -3, f(2) = -2, f(-1) = 2, f(3) = -1?

Back

f^-1(2) = -1.

Front

What is the relationship between a function and its inverse?

Back

The function and its inverse reflect over the line y = x in a coordinate plane.

Front

What is the inverse of the coordinates (3, 8) and (-3, 6)?

Back

(8, 3) and (6, -3).