If `alpha` is a real number such that `alpha>1,` then the range of the function `f(x)=(a^x-a^(-|x|))/(alpha^x+alpha^(|x|))` is

Let f (x) = log _e (sinx ), ( 0 lt x lt pi ) and g(x) = sin ^(-1) (e ^(-x)), (x ge 0) . If alpha is a positive real number such that a = ( fog)' ( alpha ) and b = (fog ) ( alpha ) , then (A) aalpha ^(2) - b alpha - a = 0 (B) a alpha ^(2) - b alpha - a = 1 (C) a alpha ^(2) + b alpha - a = - 2 alpha ^(2) (D) a alpha ^(2) + b alpha + a = 0

Find the domain of the real valued function f(x)=sqrt((x-alpha)(beta-x)),(theta lt alpha lt beta) .

The range of alpha such that range of f(x)=((x^(3)-3x+6)(x-alpha))/(2(x-alpha)) be always complete set R ,is

If sin^(x)alpha+cos^(x)alpha>=1 and 0

If alpha is a complex number and x^(2)+alpha x+bar(alpha)=0 has a real root lambda then lambda=

If f(x) = alpha x^n , prove that alpha= (f'(1))/n .

Let alpha be a real number such that 0 <= alpha <= pi. If f(x)=cosx+cos(x+alpha)+cos(x+2alpha) takes some constant number c for any x in R, then the value of [c + alpha] is equal to (Note : [y] denotes greatest integer less than or equal to y.)

Let alpha be a real number such that 0 <= alpha <= pi. If f(x)=cosx+cos(x+alpha)+cos(x+2alpha) takes some constant number c for any x in R, then the value of [c + alpha] is equal to (Note : [y] denotes greatest integer less than or equal to y.)

Let f(x)=(alpha x)/(x+1) Then the value of alpha for which f(f(x)=x is