Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if the function takes an input x and produces an output y, the inverse function takes y and produces 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 then solve for y. The resulting equation is the inverse function.

Front

What is the inverse of the function f(x) = 2x + 3?

Back

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

Front

If f(x) = x^2, what is the inverse function?

Back

f^{-1}(x) = \sqrt{x}, for x >= 0.

Front

What does it mean to switch x's and y's in finding an inverse?

Back

It means that for every point (a, b) on the graph of the function, the point (b, a) will be on the graph of the inverse function.

Front

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

Back

The inverse points are (2, 1), (4, 3).

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.

Front

What is the graphical representation of a function and its inverse?

Back

The graph of a function and its inverse are symmetric with respect to the line y = x.

Front

What is the inverse of the function g(x) = -7x^5 + 7?

Back

g^{-1}(x) = -\sqrt[5]{\frac{x - 7}{7}}.

Front

What happens to the domain and range when finding an inverse?

Back

The domain of the original function becomes the range of the inverse function, and vice versa.