Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, such that if f(x) = y, then f⁻¹(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Front

Find the inverse of f(x) = 3x + 8.

Back

f⁻¹(x) = (x - 8) / 3.

Front

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

Back

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

Front

Find the inverse of f(x) = 4 - 2x.

Back

f⁻¹(x) = 2 - ½x.

Front

Find the inverse of f(x) = 2x + 4.

Back

f⁻¹(x) = (x - 4) / 2.

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

If f(x) = x², what is the inverse function?

Back

f⁻¹(x) = √x (for x ≥ 0).

Front

What is the domain of an inverse function?

Back

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

Front

What is the range of an inverse function?

Back

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