Answer:
[tex](f*g)(x)=2x^{2}-4x-30\\[/tex]
[tex](f-g)(x)=-(x+11)\\[/tex]
Step-by-step explanation:
the expression (f*g)(x) can be expanded as follows
[tex](f*g)(x)=f(x)*g(x)\\[/tex]
since [tex]f(x)=x-5,g(x)=2x+6[/tex]
Hence
[tex](f*g)(x)=f(x)*g(x)\\(f*g)(x)=(x-5)*(2x+6)\\(f*g)(x)=2x^{2}+6x-10x-30\\(f*g)(x)=2x^{2}-4x-30\\[/tex]
also the expansion for (f-g)(x) is express as
[tex](f-g)(x)=f(x)-g(x)\\[/tex]
also since
[tex]f(x)=x-5,g(x)=2x+6[/tex] then when we substitute values, we have
[tex](f-g)(x)=(x-5)-(2x+6)\\(f-g)(x)=x-5-2x-6\\(f-g)(x)=-x-11\\(f-g)(x)=-(x+11)\\[/tex]
For this type of operation kindly note the below expansions
[tex](f*g)(x)=f(x)*g(x)\\[/tex]
[tex](f-g)(x)=f(x)-g(x)\\[/tex]
[tex](f+g)(x)=f(x)+g(x)\\[/tex]
[tex](f/g)(x)=f(x)/g(x)\\[/tex]
