For any linear function f(x)=mx+b, when does kf(x)=f(kx)?

Question

For any linear function f(x)=mx+b, when does kf(x)=f(kx)?

My options are

A. When b=0

B. when b=1

C. When m=0

D. When m=1

Answer 1

k(mx+b) = m(kx) + b

kmx + bk = kmx + b

bk = b

bk-b = 0

b(k-1) = 0

b =0 or k-1 = 0

b=0 or k=1

look like option A