Question

Given the functions f(x) = (x/3) - 12 and h(x) = x² - 1, calculate the value of the composition function (f∘h)(−2). Express the solution in proper formal format, detailing each step in the computation.

Answer 1

The value of the composition function (f∘h)(−2) is -11.

Step-by-step explanation:

To calculate the value of the composition function (f∘h)(−2), we need to substitute the value of -2 into the function h(x) = x² - 1 first.

h(-2) = (-2)² - 1 = 4 - 1 = 3.

Next, we substitute the result, which is 3, into the function f(x) = (x/3) - 12.

f(3) = (3/3) - 12 = 1 - 12 = -11.

Therefore, (f∘h)(−2) = -11.