Let's test the statement f(a+b)=f(a)+f(b) with the linear function f(x)=3x+3, and two arbitrary values, a= 1 and b= 2.
f(a+b) &⇒ f( 1+ 2)
f(a)+f(b) &⇒ f( 1)+f( 2)
Let's start by calculating f(1+2). To do so, we will substitute (1+2) for x in f(x)=3x+3.
Therefore, f(1)+f(2) equals 6+9=15.
f(1+2)=12 and f(1)+f(2)=15
Since 12 does not equal 15, we know that f(1+2)≠f(1)+f(2). Therefore, we know that it is not always true that f(a+b)=f(a)+f(b). The statement is false.
