If fx=x−2x−2+afor x 2 is continuous on R then a,b=

f(2)=5limx→2− f(x) = limn→2+f(x)limx→2− −(x−2)n−2+a = limx→2+x−2−(n−2)+6−1+a=−1+b=5a=6 b=6

If fx=x−2x−2+afor x 2 is continuous on R then a,b=

f(2)=5limx→2− f(x) = limn→2+f(x)limx→2− −(x−2)n−2+a = limx→2+x−2−(n−2)+6−1+a=−1+b=5a=6 b=6

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If $f (x) = \{\begin{cases} \frac{|x - 2|}{x - 2} + a & f o r x < 2 \\ 5 & f o r x = 2 \\ \frac{|x - 2|}{2 - x} + b & f o r x > 2 \end{cases}$ is continuous on R then $(a, b) =$

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$(- 6, 6)$

$(6, - 6)$

$(6, 6)$

$(- 6, - 6)$

answer is C.

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Detailed Solution

$f (2) = 5$
$\lim_{x \to 2^{-}} f (x) = \lim_{n \to 2^{+}} f (x)$
$\lim_{x \to 2^{-}} \frac{- (x - 2)}{n - 2} + a = \lim_{x \to 2^{+}} \frac{x - 2}{- (n - 2)} + 6$
$- 1 + a = - 1 + b = 5$
$a = 6 b = 6$

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