Let `f:R rarr[0,(pi)/(2))` defined by `f(x)=Tan^(-1)(x^(2)+x+a)` then the set of values of a for which f is onto is

Let f:R rarr[0,(pi)/(2)) be defined by f(x)=tan^(-1)(x^(2)+x+a)* Then the set of values of a for which f is onto is (a)(0,oo)(b)[2,1](c)[(1)/(4),oo](d) none of these

Let f:R rarr(0,(2 pi)/(2)] defined as f(x)=cot^(-1)(x^(2)-4x+alpha) Then the smallest integral value of alpha such that,f(x) is into function is

Let f:R rarr(0,(pi)/(6)] be defined as f(x)=sin^(-1)((4)/(4x^(2)-12x+17)) then f(x)

Let f:R rarr R be given by f(x)=(x-1)^(2)+1,xge1 . Then the set of values of x for which f(x)=f^(-1)(x) is given by

Let f:R rarr [0, (pi)/(2)) be a function defined by f(x)=tan^(-1)(x^(2)+x+a) . If f is onto, then a is equal to

Let f:[0,2]rarr[0,oo) defined as f(x)=sqrt(-x^(2)+4) ,then the values of x for which f(x)=f^(-1)(x) is

Let f:R rarr(0,(pi)/(2)) be a function defined by f(x)=cot^(-1)(x^(2)+4x+alpha^(2)-alpha), complete set of valuesof alpha for which f(x) is onto,is (A) [(1-sqrt(17))/(2),(1+sqrt(17))/(2)] (B) (-oo,(1-sqrt(17))/(2)]uu[(1+sqrt(17))/(2),oo)(C)((1-sqrt(17))/(2),(1+sqrt(17))/(2))( D) none of these

Let f(x)=lim_(nrarroo)1/((3/(pi)tan^(-1)2x)^(2n)+5) then the set of value of x for which f(x)=0 is

Let f:R rarr R be a function defined as f(x)=(x^(2)-6)/(x^(2)+2) , then f is

Let f:R rarr B be a functio defined by f(x)=tan^(-1).(2x)/(1+x^(2)) , then f is both one - one and onto when B is in the interval