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?

Back

1. Replace f(x) with y. 2. Switch x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Front

What is the inverse of the coordinates (1, 2) (3, 8) (-3, 6)?

Back

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

Front

If f(x) = x + 5, what is f⁻¹(x)?

Back

f⁻¹(x) = x - 5

Front

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

Back

f⁻¹(x) = -1/4x - 3

Front

What is the inverse of the function f(x) = 3x - 5?

Back

f⁻¹(x) = (x + 5)/3

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements. This means that each output is produced by exactly one input.

Front

What is the horizontal line test?

Back

The horizontal line test is a method to determine if a function is one-to-one. If any horizontal line intersects the graph of the function more than once, the function is not one-to-one.

Front

What is the relationship between a function and its inverse?

Back

If (a, b) is a point on the function f, then (b, a) is a point on its inverse f⁻¹.

Front

How do you verify if two functions are inverses of each other?

Back

To verify, check if f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the domain.