College Algebra, 2013a

392 Further Topics in Functions
and
(
k −1 ◦ k ) (x) = k −1 (k(x))
= k −1 (√ x +2− 1 ) , x ≥−2
= (√ x +2− 1 ) 2 +2
(√ x +2− 1
)
− 1
= (√ x +2 ) 2 − 2
√ x +2+1+2
√ x +2− 2 − 1
= x +2− 2
= x ̌
(
k ◦ k
−1 ) (x) = k ( x 2 +2x − 1 ) x ≥−1
= √ (x 2 +2x − 1) + 2 − 1
= √ x 2 +2x +1− 1
= √ (x +1) 2 − 1
= |x +1|−1
= x +1− 1 since x ≥−1
= x ̌
Graphically, everything checks out as well, provided that we remember the domain restriction
on k −1 means we take the right half of the parabola.
y
2
y = k(x) 1
−2 −1 1 2
−1
y = k −1 (x)
x
−2
Our last example of the section gives an application of inverse functions.
Example 5.2.4. Recall from Section 2.1 that the price-demand equation for the PortaBoy game
system is p(x) =−1.5x + 250 for 0 ≤ x ≤ 166, where x represents the number of systems sold
weekly and p is the price per system in dollars.