If `F :[1,oo)vec[2,oo)` is given by `f(x)=x+1/x ,t h e nf^(-1)(x)` equals. (a)`(x+sqrt(x^2-4))/2` (b) `x/(1+x^2)` (c) `(x-sqrt(x^2-4))/2` (d)`1+sqrt(x^2-4)`

If the function f:(1,oo)rarr(1,oo) is defined by f(x)=2^(x(x-1)),t h e nf^(-1)(x) is (1/2)^(x(x-1)) (b) 1/2(1+sqrt(1+4(log)_2x)) 1/2(1-sqrt(1+(log)_2x) (d) not defined

(1)/(sqrt(x^(2) + 4x + 2 ))

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (d) none of these

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]= 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a) 1/(2y-1) (b) x/(x+2y) (c) 1/(sqrt(1+4x) (d) y/(2x+y)

Expand (2x^(2)-3sqrt(1-x^(2)))^(4)+(2x^(2)+3sqrt(1-x^(2)))^(4)