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, swap the x and y in the equation 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) = 3x + 2, what is f^-1(x)?

Back

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

Front

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

Back

f^-1(x) = √x.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are reflections of each other across the line y = x.

Front

If f(x) = 5 - 2x, what is f^-1(x)?

Back

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

Front

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

Back

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

Front

How can you verify if two functions are inverses?

Back

To verify, check if f(f^-1(x)) = x and f^-1(f(x)) = x.

Front

What is the inverse of f(x) = 2x - 4?

Back

f^-1(x) = (x + 4)/2.