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Question: Range of f(x) = \(\cos ^ { - 1 } \left( \frac { 1 + x ^ { 2 } } { 2 x } \right) + \sqrt { 2 - x ^ {...

Range of f(x) = cos⁡−1(1+x22x)+2−x2\cos ^ { - 1 } \left( \frac { 1 + x ^ { 2 } } { 2 x } \right) + \sqrt { 2 - x ^ { 2 } } is

A

{0,1+π2}\left\{ 0,1 + \frac { \pi } { 2 } \right\}

B

{0, 1 + π}

C

{1,1+π2}\left\{ 1,1 + \frac { \pi } { 2 } \right\}

D

{1,1+π2}\left\{ 1,1 + \frac { \pi } { 2 } \right\}

Answer

{1,1+π2}\left\{ 1,1 + \frac { \pi } { 2 } \right\}

Explanation

Solution

is defined if ≤ 1

⇒ x ≠ 0 ⇒ 1 + x2 - 2|x| ≤ 0

⇒ (|x|− 1)2 ≤ 0 ⇒ x = 1, -1

Thus domain of f(x) is {1, -1}. Hence range

is {1, 1 + π}.