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QuestionEvaluate the function f(x)=x−2x2−7f(x)=\frac{\sqrt{x-2}}{x^{2}-7} for parts (b)-(d):
(b) Find f(−5)f(-5): A. f(−5)=f(-5)= or B. f(−5)f(-5) is undefined. (c) Find f(3.7)f(3.7): A. f(3.7)=f(3.7)= or B. f(3.7)f(3.7) is undefined. (d) Find f(−2.3)f(-2.3): A. f(−2.3)=f(-2.3)= or B. f(−2.3)f(-2.3) is undefined.

Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=x−x−7f(x)=\frac{\sqrt{x-}}{x^{}-7}

STEP 2

To evaluate f(−5)f(-5), we substitute x=−5x=-5 into the function.
f(−5)=−5−2(−5)2−7f(-5)=\frac{\sqrt{-5-2}}{(-5)^{2}-7}

STEP 3

implify the expression under the square root and in the denominator.
f(−5)=−725−7f(-5)=\frac{\sqrt{-7}}{25-7}

STEP 4

Since the square root of a negative number is not defined in the set of real numbers, we conclude that f(−)f(-) is undefined.

STEP 5

To evaluate f(3.7)f(3.7), we substitute 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 6

implify the expression under the square root and in the denominator.
f(3.)=1.13.69−f(3.)=\frac{\sqrt{1.}}{13.69-}

STEP 7

Further simplify the expression.
f(3.7)=1.76.69f(3.7)=\frac{\sqrt{1.7}}{6.69}

STEP 8

To evaluate f(−2.3)f(-2.3), we substitute x=−2.3x=-2.3 into the function.
f(−2.3)=−2.3−2(−2.3)2−7f(-2.3)=\frac{\sqrt{-2.3-2}}{(-2.3)^{2}-7}

STEP 9

implify the expression under the square root and in the denominator.
f(−2.3)=−4.35.29−7f(-2.3)=\frac{\sqrt{-4.3}}{5.29-7}

STEP 10

Since the square root of a negative number is not defined in the set of real numbers, we conclude that f(−2.3)f(-2.3) is undefined.
So, the solutions areB. f(−5)f(-5) is undefined. A. f(3.7)=.76.69f(3.7)=\frac{\sqrt{.7}}{6.69} B. f(−2.3)f(-2.3) is undefined.

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