Question

Prove or disprove: Let A,B, and C be functions of x such that C(x)=A(x)+B(x). If C(x) is linear function, then A(x) and B(x) are also linear functions.

Answer 1

easy to disprove this one

Answer 2

C(x) is linear but A(x)=sqrt(x) and B(x)=-sqrt(x) are not linear

Answer 3

Good job.

Answer 4

counterexample:
let
A(x) = x^2 + 2x+3 , B(x) = -x^2

A(x) + B(x) = 2x +3 , which is linear

Answer 5

C(x)=0*

Answer 6

That example also works.