Ummm, let us see.

f(x/m), mf(x)

I assume m is a constant.

mf(x) is m"f(x), I assume also.

f(x/m) and m*f(x) have identical graphs?

Say, m=3

And f(x/m) = f(x/3) = x^2 +2x + 6 ----(i)

What would be f(x)?

x = 3(x/3)

How are we generate the f(x)?

f(x) = (3x)^2 +2(3x) +6

f(x) = 9x^2 +6x +6 -----------(ii)

Check,

If f(x) = 9x^2 +6x +6, what is f(x/3)?

f(x/3) = 9(x/3)^2 +6(x/3) +6

f(x/3) = 9[ x^2 / 9] +2x +6

f(x/3) = x^2 +2x +6 -------same as (i).

So (ii) is okay. f(x) = 9x^2 +6x +6 ---------***

Now,

f(x/m) = f(x/3) = x^2 +2x +6 ---------(i)

mf(x) = m*f(x) = 3*f(x) = 3(9x^2 +6x +6) = 27x^2 +18x +18 ----(iii)

Would (i) and (iii) have identical graphs?

No. -----------answer.