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Let $f$ be a function defined by $2 f sin x + f cos x = x, ∀ x$ , then set of points where $f (x)$ is not differentiable is

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Set of all natural numbers

0, 1, − 1

Set of all irrational numbers

1, − 1

answer is D.

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Detailed Solution

2 f (sin x) + f (cos x) = x … (1) Re p l a c i n g x ′ b y π 2 − x 2 f (cos x) + f (sin x) = π 2 = x

Solving (1) and (2)

3 f (sin x) = 3 x − π 2 (o r) f (sin x) = x − π 6

∴ f (x) = sin − 1 x − π 6 ⇒ f ′ (x) = 1 1 − x 2

is not differentiable at x = 1, -1

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