Math Snap

STEP 1

Assumptions1. The function is defined as $f(x)=\frac{\sqrt{x-}}{x^{}-7}$
. We need to evaluate the function at $x=19$, $x=-5$, and $x=3.7$

STEP 2

First, let's evaluate $f(19)$. We can do this by substituting $x=19$ into the function.
$$f(19)=\frac{\sqrt{19-2}}{19^{2}-7}$$

STEP 3

implify the expression inside the square root and the denominator.
$$f(19)=\frac{\sqrt{17}}{361-7}$$

STEP 4

Calculate the denominator.
$$f(19)=\frac{\sqrt{17}}{354}$$

STEP 5

Now, let's evaluate $f(-5)$. We can do this by substituting $x=-5$ into the function.
$$f(-5)=\frac{\sqrt{-5-2}}{(-5)^{2}-7}$$

STEP 6

implify the expression inside the square root and the denominator.
$$f(-5)=\frac{\sqrt{-}}{25-}$$

STEP 7

Since the square root of a negative number is undefined in the real number system, we can conclude that $f(-5)$ is undefined.

STEP 8

Finally, let's evaluate $f(3.7)$. We can do this by substituting $x=3.7$ into the function.
$$f(3.7)=\frac{\sqrt{3.7-2}}{(3.7)^{2}-7}$$

STEP 9

implify the expression inside the square root and the denominator.
$$f(3.7)=\frac{\sqrt{.7}}{(3.7)^{2}-7}$$

STEP 10

Calculate the denominator.
$$f(3.7)=\frac{\sqrt{.7}}{13.69-7}$$

Calculate the final value.
$$f(3.7)=\frac{\sqrt{.7}}{6.69}$$So, the answers are(a) $f(19)=\frac{\sqrt{17}}{354}$
(b) $f(-5)$ is undefined.
(c) $f(3.7)=\frac{\sqrt{.7}}{6.69}$