If y=^{-1} x then \_\_\_\_ .

Correct Answer is : −π2<y<π2-π/2 < y < π/2−2π<y<2π

Correct Answer is : −π2<y<π2-π/2 < y < π/2−2π<y<2π

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GUJCET 2024 Math Paper (04)

Question : 15 of 40

Marks: +1, -0

y=\tan^{-1} x

\_\_\_\_

Solution:

Concept:

The principal value range of

y=\tan^{-1}x

is the open interval where

\tan y

is defined and one-to-one.

Explanation:

For

y=\tan^{-1}x

, we have

x=\tan y

The tangent function is one-to-one on the interval

-\frac{\pi}{2} < y < \frac{\pi}{2}

The endpoints

\pm\frac{\pi}{2}

are not included because

\tan y

is undefined there.

Therefore, the range of

y=\tan^{-1}x

-\frac{\pi}{2} < y < \frac{\pi}{2}

Answer:

Option C:

-\frac{\pi}{2} < y < \frac{\pi}{2}

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