The range of the function, f( x )= cot -1 x + sec -1 x + operatornamecosec-1 x, is

Question

The range of the function, f( x )= cot -1 x + sec -1 x + operatornamecosec-1 x, is (A) ((π/2), (3 π/2)) (B) ((π/2), (3 π/4)] ∪[(5 π/4), (3 π/2)) (C) [(π/2), π) ∪(π, (3 π/2)] (D) ((π/2), π) ∪(π, (3 π/2))

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/3e18769d67fb4c621f2060e0dfe051ea-.png" /> Domain of f( x ) is | x | ≥ 1 From the graph for x ≥ 1 f ( x ) can attain values from ((π/2), (3 π/4)] also for x ≤-1, f(x) can attain values from [(5 π/4), (3 π/2))

Q. The range of the function, $f (x) = cot^{- 1} x + sec^{- 1} x + cosec^{- 1} x$ , is

$(\frac{π}{2}, \frac{3 π}{2})$

$(\frac{π}{2}, \frac{3 π}{4}] \cup [\frac{5 π}{4}, \frac{3 π}{2})$

$[\frac{π}{2}, π) \cup (π, \frac{3 π}{2}]$

$(\frac{π}{2}, π) \cup (π, \frac{3 π}{2})$

Domain of $f (x)$ is $∣ x ∣ \geq 1$
From the graph for $x \geq 1 f (x)$ can attain values from $(\frac{π}{2}, \frac{3 π}{4}]$
also for $x \leq - 1, f (x)$ can attain values from $[\frac{5 π}{4}, \frac{3 π}{2})$

Q. The range of the function, f(x)=cot−1x+sec−1x+cosec−1x, is

(2π​,23π​)

(2π​,43π​]∪[45π​,23π​)

[2π​,π)∪(π,23π​]

(2π​,π)∪(π,23π​)