Let $f:\left( { - {\pi \over 4},{\pi \over 4}} \right) \to R$ be defined as $$f(x) = \left\{ {\matrix{ {{{(1 + |\sin x|)}^{{{3a} \over {|\sin x|}}}}} & , & { - {\pi \over 4} < x < 0} \cr b & , & {x = 0} \cr {{e^{\cot 4x/\cot 2x}}} & , & {0 < x < {\pi \over 4}} \cr } } \right.$$If f is continuous at x = 0, then the value of 6a + b2 is equal to :

Question

Let $f:\left( { - {\pi \over 4},{\pi \over 4}} \right) \to R$ be defined as $$f(x) = \left\{ {\matrix{ {{{(1 + |\sin x|)}^{{{3a} \over {|\sin x|}}}}} & , & { - {\pi \over 4} < x < 0} \cr b & , & {x = 0} \cr {{e^{\cot 4x/\cot 2x}}} & , & {0 < x < {\pi \over 4}} \cr } } \right.$$

If f is continuous at x = 0, then the value of 6a + b² is equal to :

1 $-$ e

e $-$ 1

1 + e

Solution

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