Remediation Inverse Functions

An inverse function reverses the effect 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.

Two functions f(x) and g(x) are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Inverse functions are reflections of each other across the line y = x.

f⁻¹(x) = (x - 3)/2.

f⁻¹(x) = √x.

The domain of the original function becomes the range of the inverse function and vice versa.

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

f⁻¹(x) = (1/3) log(x).

A function does not have an inverse if it is not one-to-one, meaning it does not pass the horizontal line test.

A function passes the horizontal line test if no horizontal line intersects the graph of the function more than once.