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) = 2x + 3?

Back

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

Front

Find the inverse of f(x) = 1/4x - 7.

Back

f^-1(x) = 4x + 28.

Front

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

Back

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

Front

What is the general form of an inverse function?

Back

If f(x) = y, then f^-1(y) = x.

Front

How do you verify if two functions are inverses?

Back

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

Front

What is the inverse of f(x) = x^2 (for x >= 0)?

Back

f^-1(x) = √x.

Front

What is the inverse of f(x) = 1/x?

Back

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

Front

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

Back

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

Front

What is the inverse of f(x) = 5x - 2?

Back

f^-1(x) = (x + 2)/5.