Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If the function f takes an input x and produces an output y, then the inverse function f⁻¹ takes y and produces the original input x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, follow these steps: 1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Front

What is the inverse of f(x) = -4x - 12?

Back

f⁻¹(x) = -1/4x - 3.

Front

What is the inverse of f(x) = 3x + 2?

Back

f⁻¹(x) = (x - 2)/3.

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) = 1/4x - 7?

Back

f⁻¹(x) = 4x + 28.

Front

What is the inverse of f(x) = 3x - 5?

Back

f⁻¹(x) = (x + 5)/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's graph across the line y = x.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse undo each other. For any x in the domain of f, f(f⁻¹(x)) = x and f⁻¹(f(x)) = x.

Front

What is the domain of an inverse function?

Back

The domain of the inverse function is the range of the original function.