phi(a*b) = phi(a) * phi(b)

f(x*y) = (x*y)^3 = x^3 * y^3 = f(x) * f(y)

thus f is a homomorphism.

kernel of phi is the mapping of the identity element of the domain, in this case the multiplicative identity which is 1 considering x to be in the set of R – {0} i.e R+.

if that is the case then kernel of f is f(1) which is 1.