K = 2 ^{-{| x + 8| - | x + 1|}} . Find the maximum value of k?

Options:

A . 234

B . 27

C . 21/7

D . 23

E . 256

Answer: Option B : B Let f(x)= (|x + 8| - | x + 1|) the expression changes to k= 2^{-f(x)} To maximize k, we need to minimize f(x) f(x) will be minimum at x=-8 and or x=-1 at x=-8, f(x)=-7 at x=-1, f(x)= 7 hence the minimum value of f(x)=-7 and so the value of k maximum will be 2^{7}

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