Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, switching the roles of inputs and outputs.

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

Find the inverse of f(x) = 2x - 2.

Back

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

Front

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

Back

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

Front

Find the inverse of f(x) = x⁴ - 2.

Back

f^-1(x) = ∜(x + 2).

Front

Find the inverse of f(x) = 3x - 5.

Back

f^-1(x) = (x + 5)/3.

Front

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

Back

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

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

What is the relationship between a function and its inverse?

Back

If f(f^-1(x)) = x and f^-1(f(x)) = x, then f and f^-1 are inverses.

Front

Can all functions have inverses?

Back

No, only one-to-one functions have inverses.