Question

On what interval is the function hx) = 1/( x-5) + 2 increasing?

A. (2, +[infinity])
B. (5, +[infinity])
C. (-[infinity], 2)
D. (-[infinity], 5)

Answer 1

The function h(x) = 1/(x-5) + 2 is increasing on the interval (5, +infinity).

Step-by-step explanation:

To determine the interval on which the function h(x) = 1/(x-5) + 2 is increasing, we need to find the values of x for which the derivative of h(x) is positive. First, find the derivative of h(x): h'(x) = -1/(x-5)2.

Since the derivative is negative for all x < 5 and positive for all x > 5, the function h(x) is increasing on the interval (5, +∞). Therefore, the correct answer is B. (5, +∞).