Inverse and Composite Functions

Front

What is the inverse of f(x) = x² - 5?

Back

f⁻¹(x) = ±√(x + 5)

Front

What is the inverse of a quadratic function?

Back

The inverse of a quadratic function is a square root function or a quadratic function with the coefficients reversed.

Front

Find the inverse of f(x) = -4x - 12.

Back

f⁻¹(x) = -1/4x - 3

Front

Given f(x) = 2x² + 5x - 17, find f(-1).

Back

f(-1) = -20

Front

Given f(x) = 2x and g(x) = x² + 3, find f(g(x)).

Back

f(g(x)) = 2x² + 6

Front

Define an inverse function.

Back

An inverse function reverses the effect of the original function, such that if f(a) = b, then f⁻¹(b) = a.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and solve for y.

Front

What is the domain of the inverse function?

Back

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

Front

What is the range of the inverse function?

Back

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