Let `f:R ->(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-sqrt17)/2,(1+sqrt17)/2]` (B) `(-infty,(1-sqrt17)/2]uu[(1+sqrt17)/2,infty)` (C) `((1-sqrt17)/2,(1+sqrt17)/2)` (D) none of these

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:[-1,1] rArr B be a function defined as f(x)=cot^(-1)(cot((2x)/(sqrt3(1+x^(2))))) . If f is both one - one and onto, then B is the interval

If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) is equal to- (a) log"(sqrt(2)+1) (b) 1 (c) 1+sqrt(2) (d) none of these

If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) is equal to- (a) log"(sqrt(2)+1) (b) 1 (c) 1+sqrt(2) (d) none of these

If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) is equal to- (a) log"(sqrt(2)+1) (b) 1 (c) 1+sqrt(2) (d) none of these

Simplify : (7)/(sqrt(17) - 2sqrt3)-( 3)/(sqrt(17) +2sqrt3)

(22) / (2sqrt (3) +1) + (17) / (2sqrt (3) -1)

If f (x) = (alpha x)/( x+1) , x ne -1 , for what value of alpha is f[f(x)] = x? a) sqrt2 b) -sqrt2 c)1 d)-1

If f'(x)=(1)/(-x+sqrt(x^(2)+1)) and f(0)=(1+sqrt(2))/(2) then f(1) is equal to -log(sqrt(2)+1)( b )11+sqrt(2)(d) none of these