[tex]\begin{gathered} f(x)+g(x)=x^2\text{ + 4x + 7} \\ \text{Domain of f(x) + g(x) }is\text{ a set of all real numbers (option D)} \end{gathered}[/tex]
Explanation:[tex]\begin{gathered} \text{GIven:} \\ f(x)\text{ = 5x + 4} \\ g(x)=x^2\text{ - x + 3} \\ \\ f(x)\text{ + g(x): we will add both function together} \end{gathered}[/tex][tex]\begin{gathered} f(x)+g(x)=5x+4+(x^2\text{ - x + 3)} \\ f(x)+g(x)=5x+4+x^2\text{ - x + 3} \\ \text{collect like terms:} \\ f(x)+g(x)=5x\text{ - x + 3 }+4+x^2 \\ f(x)+g(x)=x^2\text{ + 4x + 7} \end{gathered}[/tex][tex]\begin{gathered} \text{Domain: These are the x values} \\ \text{The function x}^2\text{ + 4x + 7 gives a parabola} \\ \text{Since there is no denominator, the domain is all real numbers} \end{gathered}[/tex]
