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 these

The range of f(x)=sin^(-1)(sqrt(x^2+x+1))i s (0,pi/2) (b) (0,pi/3) (c) [pi/3,pi/2] (d) [pi/6,pi/3]

The range of f(x)=cos^(-1)((1+x^2)/(2x))+sqrt(2-x^2) is (a) {0,1+pi/2} (b) {0,1+pi) (c) {1,1+pi/2} (d) {1,1+pi}

The range of the function tan^(-1)((x^2+1)/(x^2+sqrt(3))),x in R is a. [pi/6,pi/2) b. [pi/6,pi/3) c. [pi/6,pi/4] d. none of these

Range of tan^(-1)((2x)/(1+x^2)) is (a) [-pi/4,pi/4] (b) (-pi/2,pi/2) (c) (-pi/2,pi/4) (d) [pi/4,pi/2]

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (pi)/3 (d) (5pi)/3 (e) none of these

Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is (a) (pi/4,(3pi)/4) (b) [pi/4,(3pi)/4] (c) {pi/4,(3pi)/4} (d) none of these

Let f:[-pi/3,(2pi)/3]vec[0,4] be a function defined as f(x)=sqrt(3)sinx-cosx+2. Then f^(-1)(x) is given by (a) sin^(-1)((x-2)/2)-pi/6 (b) sin^(-1)((x-2)/2)+pi/6 (c) (2pi)/3+cos^(-1)((x-2)/2) (d) none of these

Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

The range of the function f(x)=int_(-1)^1(sinxdt)/((1-2tcosx+t^2)i s (a) [-pi/2,pi/2] (b) [0,pi] (c) {0,pi} (d) {-pi/2,pi/2}

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these