Let `f: R ->[0,pi/2)` be defined by `f(x)=tan^(-1)(x^2+x+a)dot` 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,(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 to [0, pi/2) be defined by f ( x) = tan^(-1) ( 3x^(2) + 6x + a)". If " f(x) is an onto function . then the value of a si

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)=tan^(-1)(x^(2)+x+a) . If f is onto, then a is equal to

Let f(x)=a^(x)-x ln a, a> 1. Then the complete set of real values of x for which f(x)>0 is (a)(1,oo)(b)(-1,oo)(c)(0,oo)(d)(0,1)

The function f : [0,oo)to[0,oo) defined by f(x)=(2x)/(1+2x) 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 a function f:(1, oo)rarr(0, oo) be defined by f(x)=|1-(1)/(x)| . Then f is

f:(-oo,oo)rarr(0,1] defined by f(x)=(1)/(x^(2)+1) is

f:(-(pi)/(2),(pi)/(2))rarr(-oo,oo) defined by f(x)=tan x is