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Number of integers in the integer of f(x...

Number of integers in the integer of `f(x)=1/pi(sin^(-1)x+tan^(-1)x)+(x+1)/(x^2+2x+5)` is `0` b. `3` c. `2` d. `1`

A

0

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `f(x)=(1)/(x)(sin^(-1)x+tan^(-1))+(1)/((x+1)+(4)/((x+1)))`
`=g(x)+h(x)`
where, domain of `g(x) in [-1,1]`
`therefore "Maximum value of "g(x)=g(l)=(3)/(4)` and minimum value of
`g(x)=g(-1)=-(3)/(4)`
Also, maximum value of h(x) occurs when `(x+1)+(4)/((x+1))` is
Therefore, range of f(x) is `[-(3)/(4),1]`.
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