The range of `f(x)=sin^(-1)((x^2+1)/(x^2+2))` is (a)`[0,pi/2]` (b) `(0,pi/6)` (c) `[pi/6,pi/2]` (d) none of these

Options

A. `[0,pi//2]`
B. `(0,pi//6)`
C. `[pi//6,pi//2)`
D. None of these

Answer

C

Explanation

Here, `(x^(2)+1)/(x^(2)+2)=1-(1)/(x^(2)+2)`
Now, `2 le x^(2)+2 lt oo " for all " x in R`
or ` (1)/(2) ge (1)/(x^(2)+2) gt 0`
or `-(1)/(2) le (-1)/(x^(2)+2) lt 0`
or ` (1)/(2) le 1- (1)/(x^(2)+2) lt 1`
or ` (pi)/(6) le sin^(-1)(1- (1)/(x^(2)+2)) lt (pi)/(2)`