Inverse Functions Review

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function f^-1(x) that reverses the effect of f(x). If f(a) = b, then f^-1(b) = a.

Front

How do you find the inverse of a function algebraically?

Back

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

Front

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

Back

The notation for the inverse of g(x) is g^-1(x).

Front

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

Back

The first step is to switch x and y in the equation.

Front

If f(x) = 2x + 4, what is f^-1(x)?

Back

f^-1(x) = (x - 4)/2.

Front

Are the functions f(x) = 2x + 3 and g(x) = (x - 3)/2 inverse functions?

Back

No, they are not inverse functions.

Front

What is the domain of the inverse function?

Back

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

Front

What is the range of the inverse function?

Back

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

Front

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

Back

To verify, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, ensuring that it has an inverse.