### Home > CCA2 > Chapter 5 > Lesson 5.2.5 > Problem 5-113

5-113.

For functions of the form *f*(*x*) = *mx,* it is true that *f*(*a*)* *+* f*(*b*) = *f*(*a *+* b*). For example, when *f*(*x*) = 5*x, f*(*a*)* *+* f*(*b*)* *= 5*a* + 5*b *=* *5(*a* +* b*) and *f*(*a *+* b*) = 5(*a *+* b*). Is *f*(*a*)* *+* f*(*b)* = *f*(*a *+* b*) true for all linear functions? Explain why or show why not. Homework Help ✎

Think of a linear function that has a *y*-intercept other than 0 and use it to check the relationship *f*(*a*) + *f*(*b*) = *f*(*a* + *b*).

For example, try the linear function *f*(*x*) = 2*x* + 3 (you should think of a different one for your own answer).

*f*(*a*) + *f*(*b*) = (2*a* + 3) + (2*b* + 3)*f*(*a* + *b*) = 2(*a* + *b*) + 3*f*(*a*) + *f*(*b*) = 2*a* + 2*b* + 6

But, 2*a* + 2*b* + 6 ≠ 2*a* + 2*b* + 3

*f*(*a*) + *f*(*b*) = *f*(*a* + *b*) is not true for all linear functions.