Question 1150219
I have this question that I am stuck on for my homework. It's multiple choice and I have already narrowed down one of them Thanks. Here is the question.

For any linear function f(x)=mx+b, when does 5f(x)=f(5x)+5?

A: When b=0
B: When b=5/4 
C: When b=5
D: Always

I already know that it's not C because if B equals 5 then if it gets multiplies it would not equal 5. That's all I could figure out. Thanks.
<pre><s><b><u>IGNORE the other person's answers because they're WRONG!</b></u></s> <====CORRECTED, so not needed anymore!
f(x) = mx + b
5f(x) = 5(mx + b)
5f(x) = 5mx + 5b

f(x) = mx + b
f(5x) = m(5x) + b
f(5x) = 5mx + b
f(5x) + 5 = 5mx + b + 5

Given: 5f(x) = f(5x) + 5
Therefore, 5mx + 5b = 5mx + b + 5
5b = b + 5 ------- Equating terms
5b - b = 5
4b = 5
{{{highlight_green(matrix(1,5, b, "=", 5/4, "(CHOICE", "B)"))}}}