Question

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 –4 –1 1 5 g(x) –8 –4 2 6 14 h(x) 14 8 –1 –7 –19 –4 4 negative two over three two over three

Answer 1

To determine the x-intercept of g(h(x)), we need to substitute the values of h(x) into g(x) and find the value of x for which g(h(x)) equals zero.

First, let's find the values of h(x) using the given table:

h(x): 14, 8, -1, -7, -19, -4, 4

Now, substitute these values into g(x) and find g(h(x)):

g(h(x)): g(14), g(8), g(-1), g(-7), g(-19), g(-4), g(4)

Now, let's calculate these values using the table provided:

g(14) = 14
g(8) = 6
g(-1) = 2
g(-7) = -4
g(-19) = -8 (extrapolated)
g(-4) = -4
g(4) = 6

To find the x-intercept, we need to find the value of x for which g(h(x)) equals zero. However, from the given values, there is no value of x for which g(h(x)) is zero. Therefore, the x-intercept of g(h(x)) does not exist based on the provided values.