Question

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

Answer 1

b = 5/4

Explanation:

Equations

Given the function:

`f(x)=mx+b`

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

`5f(x)=f(5x)+5`

Substituting:

`5(mx+b)=5mx+b+5`

Operating:

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

Simplifying:

`5b=b+5`

Subtracting b:

`4b = 5`

Dividing by 4:

b = 5/4