Finding Inverses of Functions

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if the function takes an input x to output y, the inverse takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

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

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

Back

The notation for the inverse of a function f(x) is f^(-1)(x).

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 all functions have inverses?

Back

No, only one-to-one functions have inverses. A function must pass the horizontal line test to be one-to-one.

Front

What is the horizontal line test?

Back

The horizontal line test states that if any horizontal line intersects the graph of a function more than once, the function does not have an inverse.

Front

What is the relationship between a function and its inverse?

Back

If f is a function and f^(-1) is its inverse, then f(f^(-1)(x)) = x and f^(-1)(f(x)) = x for all x in the domain.

Front

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

Back

To verify if two functions are inverses, compose them: f(f^(-1)(x)) should equal x and f^(-1)(f(x)) should equal x.

Front

What is the domain of the inverse function in relation to the original function?

Back

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