Inverse Functions S1 Review

Front

What is the horizontal line test used for?

Back

The horizontal line test is used to determine if a function has an inverse function. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse.

Front

How do you find the inverse of a function?

Back

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

Front

What is the notation for the inverse of a function f(x)?

Back

The inverse of the function f(x) is written as f^{-1}(x).

Front

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

Back

f^{-1}(x) = \frac{x - 2}{3}.

Front

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

Back

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

Front

If f(x) = x + 5, what is f^{-1}(x)?

Back

f^{-1}(x) = x - 5.

Front

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

Back

The first step is to replace f(x) with y.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse if it passes the horizontal line test.

Front

What is the domain of the inverse function if the original function has a range of [0, ∞)?

Back

The domain of the inverse function will be [0, ∞) if the original function has a range of [0, ∞).

Front

What is the range of the inverse function if the original function has a domain of (-∞, 5)?

Back

The range of the inverse function will be (-∞, 5) if the original function has a domain of (-∞, 5).