Determine whether the given map ∅ is a homomorphism.

Let F be the multiplicative group of all continuous functions mapping R into R that are nonzero at every x ∈ R Let R^* be the multiplicative group of nonzero real numbers. Let ∅ : F → R^* be given by ∅(f)No, it is not a homomorphism. Let f(x) = x 2 + 1. We have φ(f · f) = R 1 0 (x 2 + 1)2 dx = R 1 0 (x 4 + 2x 2 + 1)  = f₀¹f (x)dx.