An equation of the form `l a^(f(x)) + m b^(f(x)) + c =0`

An equation of the form la^(f(x))+mb^(f(x))+c=0

An equation of the form f(a^(x))=0

An equation of the form a^(f(x))+b^(f(x))=c

An equation of the form (a-f(x))^((1)/(n))+(b+f(x))^((1)/(pi))=g(x)

Let f: [a, b] -> R be a function, continuous on [a, b] and twice differentiable on (a, b) . If, f(a) = f(b) and f'(a) = f'(b) , then consider the equation f''(x) - lambda (f'(x))^2 = 0 . For any real lambda the equation hasatleast M roots where 3M + 1 is

Let f(x)=ax^(2)+bx+c, where a,b,c,in R and a!=0, If f(2)=3f(1) and 3 is a roots of the equation f(x)=0, then the other roots of f(x)=0 is

The function f satisfies the equation, f(x+y) = f(x) + f(y). Show that (a) f(0) = 0 (b) f(x) os an odd function ( c) If x is an integer and f(1) = a then, f(x)=ax.