Final answer:
To find hg(-9), substitute -9 into h(x) to find the value of h(-9), and then substitute that value into g(x) to find the value of g(h(-9)).
Step-by-step explanation:
The question asks us to find the value of hg(-9) given the functions g(x) = 4x¹⁰ and h(x) = 2x - 6.
To calculate hg(-9), we need to substitute -9 into h(x) and then substitute the result into g(x).
First, we substitute -9 into h(x):
h(-9) = 2(-9) - 6
h(-9) = -18 - 6
h(-9) = -24
Now that we have the value of h(-9) as -24, we substitute this into g(x):
g(-24) = 4(-24)¹⁰
g(-24) = 4 * (-24)¹⁰
g(-24) = 4 * (-110.08 million)
g(-24) = -440.32 million
Therefore, hg(-9) = -440.32 million.