To find \(\left(\frac{g}{h}\right)(2)\), we need to follow several steps carefully. Let's start by defining the functions and then calculating their values at \(x = 2\).
1. Define the Functions:
- \( h(x) = x + 1 \)
- \( g(x) = \sqrt{x - 2} \)
2. Evaluate the Functions at \(x = 2\):
- For \(h(x)\):
[tex]\[
h(2) = 2 + 1 = 3
\][/tex]
- For \(g(x)\):
[tex]\[
g(2) = \sqrt{2 - 2} = \sqrt{0} = 0
\][/tex]
3. Combine the Functions to Find \(\left(\frac{g}{h}\right)(2)\):
[tex]\[
\left(\frac{g}{h}\right)(2) = \frac{g(2)}{h(2)} = \frac{0}{3} = 0
\][/tex]
Therefore, the value of \(\left(\frac{g}{h}\right)(2)\) is \(0\).
So, the correct choice is:
A. [tex]\(\left(\frac{g}{h}\right)(2) = 0\)[/tex]
