Math Snap

STEP 1

Assumptions1. The function is given by $f(x)=\frac{\sqrt{x-4}}{x^{}-8}$
. We need to evaluate the function at $x=7$ and $x=-6$

STEP 2

First, let's evaluate $f(7)$. We do this by substituting $x=7$ into the function.
$$f(7)=\frac{\sqrt{7-4}}{7^{2}-8}$$

STEP 3

Now, simplify the expression inside the square root and the denominator.
$$f(7)=\frac{\sqrt{3}}{49-8}$$

STEP 4

Calculate the value in the denominator.
$$f(7)=\frac{\sqrt{3}}{41}$$So, $f(7)=\frac{\sqrt{3}}{41}$ is the correct answer for part (a).

STEP 5

Now, let's evaluate $f(-)$. We do this by substituting $x=-$ into the function.
$$f(-)=\frac{\sqrt{--4}}{(-)^{2}-8}$$

STEP 6

Now, simplify the expression inside the square root and the denominator.
$$f(-6)=\frac{\sqrt{-10}}{36-8}$$

Here, we notice that the value inside the square root is negative. In real numbers, the square root of a negative number is undefined. Therefore, $f(-6)$ is undefined.
So, $f(-6)$ is undefined is the correct answer for part (b).