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 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(1) = 3, what is f⁻¹(3)?

Back

f⁻¹(3) = 1.

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x).

Front

How can you verify if two functions are inverses of each other?

Back

To verify, check if f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the domain.

Front

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

Back

f⁻¹(x) = (x - 3)/2.

Front

What points does f⁻¹(x) go through if f(x) goes through (2, 5)?

Back

f⁻¹(x) goes through (5, 2).

Front

What is the domain of an inverse function?

Back

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

Front

What is the range of an inverse function?

Back

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