juanfranco70 juanfranco70

12-11-2020
Mathematics

contestada

For any linear function f(x) = mx + b, when does 5f(x) = f(5x) + 5? A. when b = 0 B. when b = 54 C. when b = 5 D. always

Respuesta :

elcharly64 elcharly64

13-11-2020

Answer:

b = 5/4

Step-by-step explanation:

Equations

Given the function:

[tex]f(x)=mx+b[/tex]

It's required to find the value of b such that:

[tex]5f(x)=f(5x)+5[/tex]

Substituting:

[tex]5(mx+b)=5mx+b+5[/tex]

Operating:

[tex]5mx+5b=5mx+b+5[/tex]

Simplifying:

[tex]5b=b+5[/tex]

Subtracting b:

[tex]4b = 5[/tex]

Dividing by 4:

b = 5/4

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