Function problem

If f(x) = -|-(x – 2)² + 1| - 1, and g(x) = 1/x, what is the value of (2g + f)(5)? 

A. -43/5
B. 37/5
C. -43/9
D. -53/5

First, notice that we need to combine the two functions. In other words, we must find the value of the function, that consists of the sum of twice the function of g and function f, at x = 5.

The best way is to denote a third function as a sum of the two functions g and f. If we let h(x) = 2g(x) + f(x), then we need to simply find h(5).

Now, h(x) = 2/x - |-(x – 2)² + 1| - 1. Setting x = 5, we have h(5) = 2/5 - |-(5 - 2)² + 1| - 1 = 2/5 - |-9 + 1| - 1 = 2/5 - |-8| - 1 = 2/5 - 8 - 1 = 2/5 - 9 = (2 - 45) / 5 = -43/5.

Thus the correct answer choice is (A). _________________________________________________________________________________

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