Inverse Functions

Front

What is an inverse function?

Back

An inverse function is a function that 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(x) takes y as input and produces x as output.

Front

If the domain of f(x) is x ≥ 4, what is the range of f^-1(x)?

Back

The range of f^-1(x) is y ≥ 4.

Front

In an inverse function, what elements are switched from the original function?

Back

The input and output are switched.

Front

What is the inverse of the points (1,3), (2,4), (6,8)?

Back

The inverse of the points is (3,1), (4,2), (8,6).

Front

How do you find the inverse of a function?

Back

To find the inverse of a function, swap the x and y in the equation and solve for y.

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) = 2x - 2?

Back

f^-1(x) = 1/2x + 1.

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions are inverses if applying one function followed by the other returns the original input.

Front

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

Back

f^-1(b) = a.

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across the line y = x.