Respuesta :
Solution:
Given the functions
[tex]\begin{gathered} f(x)=x^2-3 \\ g(x)=2x-1 \end{gathered}[/tex]PART 1:
Concept:
[tex](f+g)(x)=f(x)+g(x)[/tex]By applying the rule above, we will have
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=x^2-3+2x-1 \\ (f+g)(x)=x^2+2x-3-1 \\ (f+g)(x)=x^2+2x-4 \end{gathered}[/tex]To figure out (f+g)(2) means that we are going to substitute the value of x as 2
[tex]\begin{gathered} (f+g)(x)=x^2+2x-4 \\ (f+g)(2)=2^2+2(2)-4 \\ (f+g)(2)=4+4-4 \\ (f+g)(2)=4 \end{gathered}[/tex]Hence,
(f+g)(2) = 4
PART 2:
Concept:
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]By applying the rule above, we will have
[tex]\begin{gathered} (\frac{f}{g})(x)=\frac{f(x)}{g(x)} \\ (\frac{f}{g})(x)=\frac{x^2-3}{2x-1} \end{gathered}[/tex]To figure out the value of (f/g)(-1) means we will substitute the value of x=-1
[tex]\begin{gathered} (\frac{f}{g})(x)=\frac{x^2-3}{2x-1} \\ (\frac{f}{g})(-1)=\frac{(-1)^2-3}{2(-1)-1} \\ (\frac{f}{g})(-1)=\frac{1-3}{-2-1} \\ (\frac{f}{g})(-1)=\frac{-2}{-3} \\ (\frac{f}{g})(-1)=\frac{2}{3} \end{gathered}[/tex]Hence,
(f/g)(-1) = 2/3
PART 3:
To figure out the domain of (f.g)(x)
[tex](f.g)(x)=f(x)\text{.g(x)}[/tex]By applying the formula above, we will have
[tex]\begin{gathered} (f.g)(x)=f(x)\text{.g(x)} \\ (f.g)(x)=(x^2-3)(2x-1) \\ (f.g)(x)=x^2(2x-1)-3(2x-1) \\ (f.g)(x)=x^3-x^2-6x+3 \end{gathered}[/tex]Hence,
The domain of the above set of equations is given below as
[tex]=\quad \begin{bmatrix}\mathrm{Solution\colon}\: & \: -\infty\:
