function problem

Question

For any linear function f(x)=mx+b, when does 5f(x)=f(5x)+5, when does b equal 5/4

Answer 1

f(x) = mx + b

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

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

If 5f(x) = f(5x) + 5, then

5mx + 5b = 5mx + b + 5

4b = 5

b = 5/4