Question

Add and subtract functions

Answer 1

Answer:  $3x^2+5x+3$

Step-by-step explanation:

For this exercise you need to remember the multiplication of signs:

$(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-$

You know that the function f(x) is:

$f(x)=5x+3$

And the function g(x) is:  

$g(x)=3x^2$

Then to find $(f+g)(x)$ 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:

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

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

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:

$f(x) = ax^2 + bx + c$

Where "a", "b", and "c" are numbers ($a\neq 0$)