If f(x)=a x-b and g(x)=c x+d are such that f(g(x))=g(f(x)) , then which one of the following holds?

Step-by-step solution

f(x)=a x-b ....(i) and g(x)=c x+d ....(ii) aligned & f[g(x)]=g[f(x)] & a[g(x)]-b=c[f(x)]+d & a[c x+d]-b=c[a x-b]+d & [using (i) and (ii)] & a c x+a d-b=a c x-b c+d & a d-b=d-b c & a d-b+b c+d=d+d & f(d)+g(b)=2 d aligned