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 do you find the inverse of a function algebraically?

Back

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

Front

What is the graphical relationship between a function and its inverse?

Back

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

Front

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

Back

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

Front

If f(x) = 2x + 3, what is f^-1(x)?

Back

f^-1(x) = (x - 3)/2.

Front

What is the line of reflection for inverse functions?

Back

The line of reflection for inverse functions is y = x.

Front

Which of the following is NOT TRUE about inverse functions?

Back

The domain of a function always becomes the domain of its inverse.

Front

If f(x) = x², does it have an inverse? Why or why not?

Back

No, f(x) = x² does not have an inverse because it is not a one-to-one function; it fails the horizontal line test.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one. If any horizontal line intersects the graph more than once, the function does not have an inverse.

Front

If f^-1(x) = 3x - 5, what is f(x)?

Back

f(x) = (x + 5)/3.