Answer:
the condition is b= 0
Step-by-step explanation:
Given that:
The a linear function f(x) = mx + b, m ≠ 0
Recall that:
A function is a linear function if:
[tex]f(x_1 + x_2) = f(x_1) + f(x_2)[/tex]
[tex]f(cx) = cf(x)[/tex]
So, if:
[tex]f(x_1+x_2) = m(x_1+x_2) + b[/tex]
Then
[tex]f(x_1+x_2) = mx_1+mx_2+ b[/tex]
[tex]f(x_1+x_2) = f(x_1) + f(x_2) -b[/tex]
[tex]f(x_1 + x_2) = f(x_1 +x_2)[/tex] if b = 0
[tex]f(cx) = m (cx) + b[/tex]
[tex]f(cx) =c(mx) + b[/tex]
[tex]f(cx) =cf(x)[/tex] if b = 0
Therefore, the condition is b= 0
