Question number 6

Question

6. (6 pts) Given 𝑓(𝑥) = 𝑥 − 10 and 𝑔(𝑥) = |𝑥 + 7|, which of the following is the domain of the quotient function f / g ? Explain. 6._______

A. (−7, ∞)

B. (−∞,−7) ∪ (−7, 10) ∪ (10,∞)

C. (−7, 10) ∪ (10,∞)

D. (−∞, −7) ∪ (−7, ∞)

Answer 1

Remember one thing here, you can't divide a number by zero (0).

So in quotient function f / g, we get the the value of x that will make g zero and exclude that in set of real numbers. That will be our domain.

𝑔(𝑥) = |𝑥 + 7| ≠ 0

x ≠ -7

That means the domain is set of real numbers except -7. The answer is letter D.