Answer with Step-by-step explanation:
We are given that
[tex]f(x)=5x+9[/tex]
[tex]g(x)=3x^2[/tex]
f(x) is linear function
Domain of f(x)=R
g(x) is a quadratic function
Domain of g(x)=R
[tex](f+g)(x)=f(x)+g(x)=5x+9+3x^2[/tex]
Domain of (f+g)=R
(f-g)(x)=f(x)-g(x)=[tex]5x+9-3x^2[/tex]
Domain of (f-g)=R
[tex]fg(x)=f(g(x))=f(3x^2)=5(3x^2)+9=15x^2+9[/tex]
Domain of fg=R
[tex]\frac{f}{g}=\frac{5x+9}{3x^2}[/tex]
The function is not defined where g(x)=0
[tex]3x^2=0[/tex]
[tex]x=0[/tex]
Domain of f/g=R-{0}
