Studdy AI Logo
Math

QuestionEvaluate the function f(x)=x−2x2−7f(x)=\frac{\sqrt{x-2}}{x^{2}-7} for x=19x=19, x=−5x=-5, and x=3.7x=3.7. Determine if each is defined.

Studdy Solution

STEP 1

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

STEP 2

First, let's evaluate f(19)f(19). We can do this by substituting x=19x=19 into the function.
f(19)=19−2192−7f(19)=\frac{\sqrt{19-2}}{19^{2}-7}

STEP 3

implify the expression inside the square root and the denominator.
f(19)=17361−7f(19)=\frac{\sqrt{17}}{361-7}

STEP 4

Calculate the denominator.
f(19)=17354f(19)=\frac{\sqrt{17}}{354}

STEP 5

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

STEP 6

implify the expression inside the square root and the denominator.
f(−5)=−25−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)f(-5) is undefined.

STEP 8

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

STEP 10

Calculate the denominator.
f(3.7)=.713.69−7f(3.7)=\frac{\sqrt{.7}}{13.69-7}

STEP 11

Calculate the final value.
f(3.7)=.76.69f(3.7)=\frac{\sqrt{.7}}{6.69}So, the answers are(a) f(19)=17354f(19)=\frac{\sqrt{17}}{354} (b) f(−5)f(-5) is undefined. (c) f(3.7)=.76.69f(3.7)=\frac{\sqrt{.7}}{6.69}

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord