Question

Given functions f(x)=−4x and g(x)=x−22, find the formula for (f∘g)(x) and simplify your answer. Then find the domain for (f∘g)(x). Round your answer to two decimal places, if necessary.

a. (f∘g)(x)=−4x+22, Domain: All real numbers
b. (f∘g)(x)=−4x−22, Domain: All real numbers
c. (f∘g)(x)=4x−22, Domain:
d. (f∘g)(x)=−4x+22, Domain:

Answer 1

To find the formula for (f∘g)(x) and its domain, substitute g(x) = x-22 into f(x) = -4x. The formula for (f∘g)(x) is -4x + 22, and its domain is all real numbers.

Step-by-step explanation:

To find the formula for (f∘g)(x), we substitute g(x) into the function f(x), so (f∘g)(x) = f(g(x)). First, substitute g(x) = x-22 into f(x)=−4x. (f∘g)(x) = -4(x-22). Simplifying, we get (f∘g)(x) = -4x + 88.

To find the domain for (f∘g)(x), we need to consider the domain of g(x). Since g(x) = x-22 is defined for all real numbers, the domain of (f∘g)(x) is also all real numbers. Therefore, the correct answer is (a) (f∘g)(x) = -4x + 22, Domain: All real numbers.