If f : R $$ \to $$ R be defined by f (x) = e^x and g : R $$ \to $$ R be defined by g(x) = x². The mapping gof : R $$ \to $$ R be defined by (gof) (x) = g[f(x)] $$\forall $$x$$ \in $$R. Then,

For 0 $$ \le $$ p $$ \le $$ 1 and for any positive a, b; let I(p) = (a + b)^p, J(p) = a^p + b^p, then

Let $$f:R \to R$$ be such that f is injective and $$f(x)f(y) = f(x + y)$$ for $$\forall x,y \in R$$. If f(x), f(y), f(z) are in G.P., then x, y, z are in

Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19$$. Then, f(x) = 0 has