CLASSWORK Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If the function f takes an input x and produces an output y, then the inverse function f^{-1} takes y as input and produces x as output.

Front

How do you find the inverse of a function algebraically?

Back

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

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f^{-1}(x).

Front

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

Back

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

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are reflections of each other across the line y = x.

Front

Are the functions f(x) = 2x + 3 and g(x) = \frac{x - 3}{2} inverses of each other?

Back

Yes, they are inverses because g(f(x)) = x and f(g(x)) = x.

Front

What is the inverse of the function f(x) = x^2 for x >= 0?

Back

f^{-1}(x) = \sqrt{x}.

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

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

Back

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

Front

What is the inverse of the function f(x) = \frac{1}{x}?

Back

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