Graphing Calculator Math Worksheets Algebara Solver Chart Maker
 A+ A− B

## Are compositions commutative?

Does $$f(g(x)) = g(f ( x))$$ ?

## What about the composition of inverse function

In other words, what if $$f(x)$$ and $$g(x)$$ are inverses?

Practice Problems I

Directions: : Evaluate each composition of functions listed below.
Problem 1) Let $$f(x) = x + 3$$ and $$g(x) = 4x$$.
Evaluate $$f( g( 2))$$
 Step 1

Problem 2) Let $$f(x) = x^2$$ and $$g(x) = x+1$$.
Evaluate $$(f \cdot g)( 8)$$
 Step 1

Problem 3) Let $$f(x) = | 7x + 4 |$$ and $$h(x) = \sqrt{2x}$$.
Evaluate $$(f \cdot h)( 18)$$
 Step 1
Practice Problems II

Problem 1) Let $$k(x) = x^2 + x$$ and $$h(x) = x + 3$$.
Evaluate $$(k \cdot h)( x )$$
Problem 1) Let $$g(x) = 2x^2 - 3x$$ and $$h(x) = x + 4$$.
Evaluate $$(g \cdot h)( x )$$