Inverse and Composite Functions

Front

What is the inverse of f(x) = x² - 5?

Back

f⁻¹(x) = ±√(x + 5)

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

f⁻¹(x) = -1/4x - 3

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

f(-1) = -20

Tags

CCSS.HSF.IF.A.2

Front

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

Back

f(g(x)) = 2x² + 6

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.B.4A

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)).

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.B.4A

Front

What is the domain of the inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

What is the range of the inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C