Studdy AI Logo
Math

QuestionEvaluate the function f(x)=x−4x2−8f(x)=\frac{\sqrt{x-4}}{x^{2}-8} for f(7)f(7), f(−6)f(-6), and f(4.3)f(4.3).

Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=x−4x−8f(x)=\frac{\sqrt{x-4}}{x^{}-8} . We need to evaluate f(7)f(7), f(−6)f(-6), and f(4.3)f(4.3)3. We will use the given function to find the values

STEP 2

First, let's evaluate f(7)f(7). Substitute x=7x=7 into the function.
f(7)=7−472−8f(7)=\frac{\sqrt{7-4}}{7^{2}-8}

STEP 3

implify the expression inside the square root and the denominator.
f(7)=349−8f(7)=\frac{\sqrt{3}}{49-8}

STEP 4

Further simplify the denominator.
f(7)=341f(7)=\frac{\sqrt{3}}{41}So, f(7)=341f(7)=\frac{\sqrt{3}}{41} is the correct answer for part (a).

STEP 5

Next, let's evaluate f(−)f(-). Substitute x=−x=- into the function.
f(−)=−−4(−)2−8f(-)=\frac{\sqrt{--4}}{(-)^{2}-8}

STEP 6

implify the expression inside the square root and the denominator.
f(−6)=−1036−8f(-6)=\frac{\sqrt{-10}}{36-8}

STEP 7

Since the square root of a negative number is undefined in the real number system, we can conclude that f(−6)f(-6) is undefined.
So, f(−6)f(-6) is undefined is the correct answer for part (b).

STEP 8

Finally, let's evaluate f(4.3)f(4.3). Substitute x=4.3x=4.3 into the function.
f(4.3)=4.3−4(4.3)2−8f(4.3)=\frac{\sqrt{4.3-4}}{(4.3)^{2}-8}

STEP 9

implify the expression inside the square root and the denominator.
f(4.3)=.318.49−8f(4.3)=\frac{\sqrt{.3}}{18.49-8}

STEP 10

Further simplify the denominator.
f(4.3)=0.310.49f(4.3)=\frac{\sqrt{0.3}}{10.49}So, f(4.3)=0.310.49f(4.3)=\frac{\sqrt{0.3}}{10.49} is the correct answer for part (c).

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