Question

Given f (x )equals 5 x plus 9 and g (x )equals 3 x squared​, first find f plus g​, f minus g​, ​fg, and StartFraction f Over g EndFraction . Then determine the domain for each function.

Answer 1

Answer with Step-by-step explanation:

We are given that

$f(x)=5x+9$

$g(x)=3x^2$

f(x) is linear function

Domain of f(x)=R

g(x) is a quadratic function

Domain of g(x)=R

$(f+g)(x)=f(x)+g(x)=5x+9+3x^2$

Domain of (f+g)=R

(f-g)(x)=f(x)-g(x)=$5x+9-3x^2$

Domain of (f-g)=R

$fg(x)=f(g(x))=f(3x^2)=5(3x^2)+9=15x^2+9$

Domain of fg=R

$\frac{f}{g}=\frac{5x+9}{3x^2}$

The function is not defined where g(x)=0

$3x^2=0$

$x=0$

Domain of f/g=R-{0}