1.

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

Answer» Correct Answer - C
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)`


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