Inverse Functions

Front

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

Back

The x's and y's are switched.

Front

What is the inverse of the function f(x) = 3x?

Back

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

Front

What does an inverse function do?

Back

Does the opposite of the original function.

Front

If f(x) = 3x + 10, what is f^-1(x)?

Back

f^-1(x) = (x - 10)/3.

Front

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

Back

f^-1(x).

Front

If g(x) = ⅓x - 3, what is g^-1(x)?

Back

g^-1(x) = 3x + 9.

Front

What is the relationship between a function and its inverse?

Back

The inverse function reverses the effect of the original function.

Front

How do you find the inverse of a function algebraically?

Back

Replace f(x) with y, switch x and y, and solve for y.

Front

What is the graphical representation of an inverse function?

Back

It is a reflection of the original function across the line y = x.

Front

If f(x) = x², does it have an inverse?

Back

No, because it is not one-to-one.