`g(x)=(x)/(x-2) and h(x)=sqrt(9-x)`
Given of the following defined above, what is the value of `(g@h)(5)`?

Options

A. `0`
B. `(8)/(7)`
C. `2`
D. Undefined

Explanation

To find the value of \((g \circ h)(5)\), we need to follow these steps:

1. **Calculate \(h(5)\)**:
The function \(h(x)\) is defined as:
\[ h(x) = \sqrt{9 - x} \]
Substituting \(x = 5\):
\[ h(5) = \sqrt{9 - 5} = \sqrt{4} = 2 \]

2. **Calculate \(g(h(5))\)**:
Now we need to find \(g(h(5))\), which is \(g(2)\) since \(h(5) = 2\).
The function \(g(x)\) is defined as:
\[ g(x) = \frac{x}{x - 2} \]
Substituting \(x = 2\):
\[ g(2) = \frac{2}{2 - 2} = \frac{2}{0} \]
Since division by zero is undefined, \(g(2)\) is undefined.

3. **Conclusion**:
Therefore, \((g \circ h)(5) = g(h(5)) = g(2)\) is undefined.

### Final Answer:
\((g \circ h)(5)\) is undefined.