Evaluating a Composition of Functions Solutions

• As with combinations, you can evaluate functions using:

  • a    graph   
  • 
a    given value   
  • 
an    expression    

• Remember that    continuous    functions extend infinitely, meaning that a composition’s solution may lie    outside    the visible graph.

• In these instances, use    substitution    to algebraically evaluate a composition of functions for given values or expressions.

Example 3

Nancy and Sam want to purchase a $1100 refrigerator from a store that allows them to stack coupons. Nancy found a $150 off coupon, and Sam found a 15% off coupon. What composition of applying the coupons will result in the lowest purchase price?

x: price
Let f(x) = x – 150
Let g(x) = (1.00 – 0.15)(x) = 0.85(x)

Nancy and Sam should apply the 15% off coupon and then a $150 off coupon for the lowest price.

Example 4

Evaluate: $\left[b\circ a\right]\left(\frac{c}{4}\right)$

$a\left(x\right)=3x+2 b\left(x\right)=x^2+x$

Example 5

Evaluate. Use the graph or evaluate algebraically.

$j\left(x\right)={\left(x–2\right)}^3–4 k\left(x\right)=–3x+2$