Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^-1(y) takes y back to x.

Front

How is the inverse of a function denoted?

Back

The inverse of a function f(x) is denoted as f^-1(x).

Front

What is the relationship between a function and its inverse?

Back

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

Front

What does it mean for two functions to be inverses?

Back

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

How can you find the inverse of a function algebraically?

Back

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

Front

What is the domain of an inverse function?

Back

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

Front

What is the range of an inverse function?

Back

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

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is obtained by reflecting the graph of the original function over the line y = x.

Front

If f(3) = 7, what is f^-1(7)?

Back

f^-1(7) = 3.

Front

What is the significance of the line y = x in relation to inverse functions?

Back

The line y = x serves as the line of reflection for a function and its inverse.