The Range of The function f x - sec -1 x is -A- 0- -B- 0- - 2C- - 2- - 2-0D- - 2- - 2

The correct option is B 0, nbsp;π nbsp; nbsp;π2The Range of nbsp;sec 1 is nbsp;0,π nbsp; nbsp;π2. ...

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Factors Determining Choice of Form of Organisation

The Range of ...

Question

The Range of The function $f (x) = {sec}^{- 1} x$ is .

(0, π)

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(0, π] - (\frac{π}{2}}

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(\frac{- π}{2}, \frac{π}{2}] - (0}

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(\frac{- π}{2}, \frac{π}{2})

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(a) [- \frac{π}{2}, \frac{π}{2}] - \{0\} (b) [0, π] - \{\frac{π}{2}\} (c) (0, π) (d) (- \frac{π}{2}, \frac{π}{2})

{sin}^{- 1} (2^{x})

(- \frac{π}{2}, \frac{π}{2}) (b) [0, π] - \{\frac{π}{2}\} (c) [- \frac{π}{2}, \frac{π}{2}] (d) [- \frac{π}{2}, \frac{π}{2}] - \{0\}

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 2 sin x, & - π \leq x \leq \frac{- π}{2} a cos (x) + b, & \frac{- π}{2} < x < 0 - 2 + cos x, & 0 \leq x \leq \frac{π}{2} c sin x, & \frac{π}{2} < x \leq π \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

[- π, π],

f (x)

f (x) = \int_{0}^{1} t sin (x + π t) d t, x \in R

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