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Question: Range of ƒ(x) = sin<sup>–1</sup> x + tan<sup>–1</sup> x + sec<sup>–1</sup> x is-...

Range of ƒ(x) = sin–1 x + tan–1 x + sec–1 x is-

A

(π4,3π4)\left( \frac{\pi}{4},\frac{3\pi}{4} \right)

B

[π4,3π4]\left\lbrack \frac{\pi}{4},\frac{3\pi}{4} \right\rbrack

C

{π4,3π4}\left\{ \frac{\pi}{4},\frac{3\pi}{4} \right\}

D

None of these

Answer

{π4,3π4}\left\{ \frac{\pi}{4},\frac{3\pi}{4} \right\}

Explanation

Solution

ƒ(x) = sin–1 x + tan–1 x + sec–1 x clearly domain of f(x) is

x = ±1. Thus range clearly of ƒ(x) is {ƒ(1), ƒ(–1)}̃ {π4,3π4}\left\{ \frac{\pi}{4},\frac{3\pi}{4} \right\}