Question

for some a,b,c ∈ $\N$, let f(x) = ax-3 and g(x)=xb+c, x ∈ $\R$. If (fog)-1 (x) = $(\frac{x-7}{2})^{\frac{1}{3}}$ then (fog) (ac) + (gof) (b) is equal to _________ .

Answer 1

The correct answer is 2039
Let fog(x)=h(x)

⇒h−1(x)=(2x−7​)31​

⇒h(x)= fog (x)=2x3+7
fog (x)=a(xb+c)−3

⇒a=2,b=3,c=5

⇒fog(ac)=fog(10)=2007
g(f(x)=(2x−3)3+5
⇒gof(b)=gof(3)=32
⇒sum=2039