Question

Let g(x) = 2x and h(x) = x2 + 4.

Evaluate (hg)(-5).


104


250


146


-246

Answer 1

The composite function (hg)(-5) is evaluated by first applying g(x) to the input of -5, getting -10, and then applying h(x) to -10, yielding a result of 104.

Step-by-step explanation:

The function (hg) is a composition of two functions, h(x) and g(x). This means we first apply g to our input, and then apply h to the result of g. Let's evaluate (hg)(-5) step by step:

1. First, evaluate g(-5) = 2(-5) = -10.
2. Second, take that result and plug it into h, so we evaluate h(-10).
3. The function h(x) is defined as x2 + 4, so h(-10) = (-10)2 + 4 = 100 + 4 = 104.

Thus, (hg)(-5) = 104.

Answer 2

To evaluate (hg)(-5), we first find g(-5) which is -10, and then calculate h(-10), resulting in 104 as the final answer.

Step-by-step explanation:

To evaluate (hg)(-5), we need to substitute x with -5 in the function g(x), and then use that result as the input for the function h(x).

1. First, evaluate g(-5):
   g(-5) = 2(-5) = -10.
2. Next, use -10 as input for h(x):
   h(-10) = (-10)2 + 4 = 100 + 4 = 104.

Therefore, the result of (hg)(-5) is 104.