Question

Given: g(x) = √ x− 3 and ℎ(x) = 2x − 7.

a) What are the restrictions on the domain of g° ℎ? Show your work for full credit.

xx ≥ _____________


b) What is g(ℎ(13))? Simplify your answer in lowest terms. Show your work for full credit

Answer 1

Restrictions on the domain: x>=5

g(h(13)) = ±4

Explanation:

g° ℎ is the composite function

We stick the function h in for x in the function g

g(x) = sqrt(x-3)

h(x) = 2x-7)

g(h(x)) = sqrt( 2x-7 -3)

g(h(x)) = sqrt( 2x-10)

The restrictions on the domain , or the allowed values of x

sqrt (2x-10) >= 0

Square each side

2x-10 >= 0

2x>= 10

Divide by 2

x>=5

Let x=13

g(h(13)) = sqrt( 2*13-10)

sqrt(26-10)

sqrt(16)

±4