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Let f(x)= cos^(-1)((x^(2))/(x^(2)+1)). T...

Let `f(x)= cos^(-1)((x^(2))/(x^(2)+1))`. Then , the range of the f , is

A

`(0, pi//2]`

B

`[-pi//2, pi//2]`

C

`[-pi//2, 0]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Since `0 le (x^(2))/(x^(2) + 1) lt 1` for all `x in R`. Therefore
`0 lt cos^(-1) ((x^(2))/(x^(2)+1)) lt (pi)/(2)`
` 0 lt f(x) le (pi)/(2) rArr` Range of `f(x) = (0,pi//2)]`
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