Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, switching the input and output.

Front

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

Back

f^-1(x) = x - 5.

Front

What does it mean to find the inverse of a function?

Back

It means to switch the x's and y's.

Front

What is the inverse of the points (1,3), (2,4), (6,8)?

Back

(3,1), (4,2), (8,6).

Front

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

Back

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

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, switch x and y, and solve for y.

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f^-1(x).

Front

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

Back

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

Front

What is the graphical representation of an inverse function?

Back

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

Front

If f(x) = x², is f^-1(x) defined for all x?

Back

No, f^-1(x) is not defined for all x because f(x) is not one-to-one.