Which of the following is true about the function below? 1/sqrt(x-6) a. its domain is (6,infinity) and its range is (- infinity, infinity) b. its domain is (6,infinity) and its range is (- infinity, 0) u (0, infinity) c. its domain is (- infinity, 0) and its range is (0, infinity) d. its domain is (6,infinity) and its range is (0, infinity)

the answer is b, its domain is (6, infinity) and its range is (-infinity, 0) u (0, infinity). the domain is so because of the square root, which cannot be answered rationally if its negative. therefore, x-6> =0, which starts being true when x is 6 until infinity. the range is thus because the equation will be undefined at 0, since 1/0 is undefined.

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step-by-step explanation:

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).