Let f(x) be a polynomial one-one function such that
f(x)f(y)+2=f(x)+f(y)+f(xy),∀x,y∈R−{0},f(1)=1,f′(1)=3.
Let g(x)=4x(f(x)+3)−∫0xf(t)dt , then
a. g(x)=0 has exactly one root for x∈(0,1)
b. g(x)=0 has exactly two roots for x∈(0,1)
c. g(x)=0,∀x∈R−{0}
d. g(x)=0,∀x∈R−{0}