Answer:
[tex](f-g)(x)=-x^2+x+6[/tex]
Domain:
[tex](-\infty,\infty)[/tex]
Step-by-step explanation:
we are given
[tex]f(x)=9-x^2[/tex]
[tex]g(x)=3-x[/tex]
Calculation of (f-g)(x):
[tex](f-g)(x)=f(x)-g(x)[/tex]
we can plug it
[tex](f-g)(x)=9-x^2-(3-x)[/tex]
now, we can simplify it
[tex](f-g)(x)=9-x^2-3+x[/tex]
[tex](f-g)(x)=6-x^2+x[/tex]
[tex](f-g)(x)=-x^2+x+6[/tex]
Domain:
we know that
domain is all possible values of x for which any function is defined
and f(x),g(x) and (f-g)(x) are polynomials
so, domain will be all real numbers
so, we get
[tex](-\infty,\infty)[/tex]
