Question

29

02.04 MC)
Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x)). (5 points)
X -6
02.09 Applications of Functions Exam Part One
Pre-Calculus $1 v21 23-24/ Module 02: Applications of Functions
-5
g(x) 16
10 1 -5 -17
h(x) -11 -7 -1 3 11
5
-4 -1 1 5

Answer 1

To determine the x-intercept of g(h(x)), substitute the values of h(x) into g(x) and find where g(h(x)) equals zero. After performing the calculations, the x-intercept is found to be x = -1.

Step-by-step explanation:

To find g(h(x)), substitute each value of h(x) into g(x) and calculate the corresponding g(h(x)).

`For x = -11: \(g(h(-11)) = g(16) = 16\)\For x = -7: \(g(h(-7)) = g(10) = 10\)\For x = -1: \(g(h(-1)) = g(-5) = -17\)\For x = 3: \(g(h(3)) = g(11) = 11\)\For x = 11: \(g(h(11)) = g(5) = -4\)`

The x-intercept occurs when g(h(x)) equals zero. In this case,
`\(g(h(x)) = 0\)`for x = -1. Therefore, the x-intercept of
`g(h(x))` is at x = -1.

Understanding the composition of functions is crucial for this calculation. The process involves substituting the values of h(x) into g(x) to obtain a new function g(h(x)). By identifying where this composite function equals zero, we determine the x-intercept.