Range of f(x) = sin-1x + tan-1x + cos−1x is | MATH - FUNCTIONS | SolveeIt

Range of f(x) = sin^-1x + tan^-1x + cos⁻¹x is

$\left( 0 , \frac { 3 \pi } { 2 } \right)$

$\left( \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right)$

$\left( - \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } \right]$

$\left[ \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right]$

Answer

$\left[ \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right]$

Explanation

Clearly the domain of the function is [-1, 1]. We know that tan⁻¹ x ∈ $\left[ - \frac { \pi } { 4 } , \frac { \pi } { 4 } \right]$ for

x ∈ [-1, 1]. Thus range is $\left[ \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } \right]$

Question: Range of f(x) = sin<sup>-1</sup>x + tan<sup>-1</sup>x + cos<sup>−1</sup>x is...