Inverse Functions

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

How do you find the inverse of a set of coordinates?

Back

To find the inverse of a set of coordinates, switch the x and y values of each coordinate. For example, the inverse of (1, 2) is (2, 1).

Front

If a function f(x) passes through the points (-1, 4) and (4, 6), what points does its inverse f^-1(x) pass through?

Back

The inverse f^-1(x) will pass through the points (4, -1) and (6, 4).

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. For example, f(f^-1(x)) = x.

Front

What is the first step to solve for x in the equation x² = 9?

Back

The first step is to take the square root of both sides.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function's graph across the line y = x.

Front

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

Back

You can verify if two functions are inverses by checking if f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.

Front

What is the domain of an inverse function?

Back

The domain of an inverse function is the range of the original function.

Front

What is the range of an inverse function?

Back

The range of an inverse function is the domain of the original function.

Front

What is the significance of the horizontal line test in relation to inverse functions?

Back

The horizontal line test determines if a function is one-to-one, which is necessary for it to have an inverse.