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

If f(x) = 2x + 3, what is f^-1(x)?

Back

f^-1(x) = (x - 3)/2.

Front

What is the domain of the function f(x) = x + 5?

Back

The domain is all real numbers, (-∞, ∞).

Front

What is the range of the function f(x) = x + 5?

Back

The range is also all real numbers, (-∞, ∞).

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

Are the functions f(x) = x + 2 and g(x) = x - 2 inverses of each other?

Back

No, they are not inverses because f(g(x)) does not equal x.

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 two functions to be inverses?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the first step in finding the inverse of a function?

Back

Replace f(x) with y.