Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, such that if f(x) = y, then f⁻¹(y) = x.

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 the coordinates (1, 2) (3, 8) (-3, 6)?

Back

(2, 1) (8, 3) (6, -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

Find the inverse of f(x) = 2x - 2.

Back

f⁻¹(x) = 1/2x + 1.

Front

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

Back

(3, 1)(4, 2)(8, 6).

Front

If f(x) = 3x + 5, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 5)/3.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse undo each other; applying one after the other returns the original value.

Front

How can you verify if two functions are inverses?

Back

If f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the domain.