Answer: [tex]3x^2+5x+3[/tex]
Step-by-step explanation:
For this exercise you need to remember the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]
You know that the function f(x) is:
[tex]f(x)=5x+3[/tex]
And the function g(x) is:
[tex]g(x)=3x^2[/tex]
Then to find [tex](f+g)(x)[/tex] you need to add the function f(x) and the function g(x) by adding (or combining) the like terms, you get that the sum is the following:
[tex](f+g)(x)=(5x+3)+(3x^2)[/tex]
[tex](f+g)(x)=5x+3+3x^2\\\\(f+g)(x)=3x^2+5x+3[/tex]
As you can notice, when you add the functions given in the exercise, you get a Quadratic function, which is a function whose highest exponent is 2 and has this form:
[tex]f(x) = ax^2 + bx + c[/tex]
Where "a", "b", and "c" are numbers ([tex]a\neq 0[/tex])
