SOLUTION: 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

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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.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
f(x) = mx + b

5f(x) = 5mx + 5b

f(5x) + 5 = [5mx + b] + 5

they're equal when 5mx + 5b = 5mx + b + 5
5mx cancels out and you are left with:
5b = b + 5
subtract b from both sides to get:
4b = 5
solve for b to get:
b = 5/4









Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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.
IGNORE the other person's answers because they're WRONG! <====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

 

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