sekushijojo
Answered

Given that [tex]$h(x)=x+1[tex]$[/tex] and [tex]$[/tex]g(x)=\sqrt{x-2}$[/tex], find [tex]\left(\frac{g}{h}\right)(2)[/tex], if it exists.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice:

A. [tex]\left(\frac{ g }{ h }\right)(2) = \ \square[/tex] (Simplify your answer.)

B. The function value does not exist.



Answer :

GinnyAnswer
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]