Let `x=1/3`or `x=-15` satisfies the equation, `log_g(kx^2+ wx+ f)= 2`. If `k, w` and `f` are relatively prim positive integers then find the value of `k+w+f`.

Let y =f (x) satisfies the differential equation xy (1+y) dx =dy . If f (0)=1 and f (2) =(e ^(2))/(k-e ^(2)), then find the value of k.

Let y =f (x) satisfies the differential equation xy (1+y) dx =dy . If f (0)=1 and f (2) =(e ^(2))/(k-e ^(2)), then find the value of k.

f(x) = log((1+x)/(1-x)) satisfies the equation: f(x_(1)) +f(x_(2))

If f(x)=3x-2, g(x)=2x+k and if fog=gof, then find the value of k.

If f(x)=x^(3)+x^(2)+kx+4 is always increasing then least positive integral value of k is

If f(x)=x^(3)+x^(2)+kx+4 is always increasing then least positive integral value of k is

If x +2 is a factor of f( x) and f(x) =x^(3)+4x^(2)+kx-6 , then find the value of k .

int_(0)^( pi)sqrt((cos x+cos2x+cos3x)^(2)+(sin x+sin2x+sin3x)^(2))dx is equal to ((pi)/(k)+w), where k and w are positive integers,find the value of (k^(2)+w^(2))