A function f(x) is defined as where Which one of the

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A function f(x) is defined as
where
Which one of the following statements is TRUE?

[GATE EE 2017 Set 1]

A f(x) is NOT differentiable at x=1 for any values of a and b.

B f(x) is differentiable at x = 1 for the unique values of a and b

C f(x) is differentiable at x = 1 for all values of a and b such that a + b = e

D f(x) is differentiable at x = 1 for all values of a and b.