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Many-One into Function

integrate (0 ...

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integrate (0 to 3): f(x) dx where f(x)= {cos2x, 0=3

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f (x) = sin (log x)

y = f (\frac{2 x + 3}{3 - 2 x})

\frac{d y}{d x}

Q. Assertion :Let

f (x) = {cos}^{2} x + {cos}^{2} (x + \frac{π}{3}) + {cos}^{2} (x - \frac{π}{3})

f^{'} (x) = 0

. Reason: Derivative of a constant function is always zero.

f^{''} (x) = \frac{cos (log x)}{x}

f^{'} (1) = 0

y = f (\frac{2 x + 3}{3 - 2 x})

\frac{d y}{d x}

f_{1} (x) = {sin}^{- 1} (cos ({sin}^{2} x)),

f_{2} (x) = {cos}^{- 1} (sin ({cos}^{2} x)),

f_{3} (x) = {sin}^{- 1} (cos ({cos}^{2} x))

f_{4} (x) = {cos}^{- 1} (sin ({sin}^{2} x)) .

Then which of the following is (are) CORRECT?

f (x)

is the integral of

\frac{2 sin x - sin 2 x}{x^{3}}, x \neq 0

{lim}_{x \to 0} f^{^{'}} (x)

f^{^{'}} (x) = \frac{d f (x)}{d x}

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Many-One into Function

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