FunctionHard

Question

Let f : R → R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true?

Options

A.f(x) ≥ 1 for all x ∈ R
B.f(x) is not differentiable at x = 1
C.f(x) is differentiable everywhere
D.f(x) is not differentiable at x = 0

Solution

         
f(x) = min{x + 1, |x| + 1}
f(x) = x + 1 ∀ x ∈ R.

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