f(x)=2x+2−164x−16is continuous at X=2then f(2)=

f(2)=Ltx→2f(x)=Ltx→22x+2−164x−16=Ltx→22x.4−16(2x)2−16=Ltx→24|2x−4|(2x+4)(2x−4)=Ltx→242x+4=48=12

f(x)=2x+2−164x−16is continuous at X=2then f(2)=

f(2)=Ltx→2f(x)=Ltx→22x+2−164x−16=Ltx→22x.4−16(2x)2−16=Ltx→24|2x−4|(2x+4)(2x−4)=Ltx→242x+4=48=12

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$f (x) = \frac{2^{x + 2} - 16}{4^{x} - 16}$ is continuous at $X = 2$ then $f (2) =$

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$\begin{array}{l} 1 \\ \bar{3} \end{array}$

$\begin{array}{l} 1 \\ \bar{2} \end{array}$

answer is D.

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Detailed Solution

$f (2) = \underset{x \to 2}{L t} f (x)$

$= \underset{x \to 2}{L t} \frac{2^{x + 2} - 16}{4^{x} - 16}$

$= \underset{x \to 2}{L t} \frac{2^{x} .4 - 16}{{(2^{x})}^{2} - 16}$

$= \underset{x \to 2}{L t} \frac{4 | 2^{x} - 4 |}{(2^{x} + 4) (2^{x} - 4)} = \underset{x \to 2}{L t} \frac{4}{2^{x} + 4} = \frac{4}{8} = \frac{1}{2}$

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$f (x) = \frac{2^{x + 2} - 16}{4^{x} - 16}$ is continuous at $X = 2$ then $f (2) =$