QuestionEvaluate $f(19)$ for the function $f(x)=\frac{\sqrt{x-2}}{x^{2}-7}$ . Is it defined or undefined?

Studdy Solution

STEP 1

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

STEP 2

To evaluate $f(19)$ , we need to substitute $x=19$ into the function.
$f(19)=\frac{\sqrt{19-2}}{19^{2}-7}$

STEP 3

Now, simplify the expression inside the square root and the denominator.
$f(19)=\frac{\sqrt{17}}{19^{2}-7}$

STEP 4

Calculate the value of the denominator.
$f(19)=\frac{\sqrt{17}}{361-7}$

STEP 5

Further simplify the denominator.
$f(19)=\frac{\sqrt{17}}{354}$ So, the correct answer is A. $f(19)=\frac{\sqrt{17}}{354}$ .

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QuestionEvaluate $f(19)$ for the function $f(x)=\frac{\sqrt{x-2}}{x^{2}-7}$ . Is it defined or undefined?

Studdy Solution

STEP 1

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

STEP 2

To evaluate $f(19)$ , we need to substitute $x=19$ into the function.
$f(19)=\frac{\sqrt{19-2}}{19^{2}-7}$

STEP 3

Now, simplify the expression inside the square root and the denominator.
$f(19)=\frac{\sqrt{17}}{19^{2}-7}$

STEP 4

Calculate the value of the denominator.
$f(19)=\frac{\sqrt{17}}{361-7}$

STEP 5

Further simplify the denominator.
$f(19)=\frac{\sqrt{17}}{354}$ So, the correct answer is A. $f(19)=\frac{\sqrt{17}}{354}$ .

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QuestionEvaluate f(19)f(19)f(19) for the function f(x)=x−2x2−7f(x)=\frac{\sqrt{x-2}}{x^{2}-7}f(x)=x2−7x−2​​. Is it defined or undefined?

Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=x−x−7f(x)=\frac{\sqrt{x-}}{x^{}-7}f(x)=x−7x−​​ . We need to evaluate f(19)f(19)f(19)

STEP 2

To evaluate f(19)f(19)f(19), we need to substitute x=19x=19x=19 into the function.f(19)=19−2192−7f(19)=\frac{\sqrt{19-2}}{19^{2}-7}f(19)=192−719−2​​

STEP 3

Now, simplify the expression inside the square root and the denominator.f(19)=17192−7f(19)=\frac{\sqrt{17}}{19^{2}-7}f(19)=192−717​​

STEP 4

Calculate the value of the denominator.f(19)=17361−7f(19)=\frac{\sqrt{17}}{361-7}f(19)=361−717​​

STEP 5

Further simplify the denominator.f(19)=17354f(19)=\frac{\sqrt{17}}{354}f(19)=35417​​So, the correct answer is A. f(19)=17354f(19)=\frac{\sqrt{17}}{354}f(19)=35417​​.

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QuestionEvaluate $f(19)$ for the function $f(x)=\frac{\sqrt{x-2}}{x^{2}-7}$ . Is it defined or undefined?

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

To evaluate $f(19)$ , we need to substitute $x=19$ into the function.
$f(19)=\frac{\sqrt{19-2}}{19^{2}-7}$

Now, simplify the expression inside the square root and the denominator.
$f(19)=\frac{\sqrt{17}}{19^{2}-7}$

Calculate the value of the denominator.
$f(19)=\frac{\sqrt{17}}{361-7}$

Further simplify the denominator.
$f(19)=\frac{\sqrt{17}}{354}$ So, the correct answer is A. $f(19)=\frac{\sqrt{17}}{354}$ .