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`

Options

A. 0
B. 3
C. 2
D. 1

Answer

C

Explanation

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]`.