Question

If f(x)=x over 2-3 and g(x)=3x^2+x-6 find (f+g)(x)

Answer 1

`(f + g) (x) =3x^(2) +(3)/(2)x-9`

Explanation:

We are given the following two functions and we are to add them:

`f (x) = \frac {x} {2} -3`

`g (x) = 3x^(2) + x - 6`

Adding these two functions, we get:

`(f + g) (x) = f (x) + g (x)`

`(f + g) (x) = \frac {1} {2} x - 3 + 3x^(2) + x - 6`

Adding the like terms together and simplifying them to get:

`(f + g) (x) = 3x^(2) + \frac {3}{2} x - 9`

Answer 2

`(f + g)(x) = 3x ^ 2 + (3)/(2)x - 9`

Explanation:

We are asked to find (f + g) (x)

In this case what we must do is add the function f (x) with the function g (x). So, we have:

`f(x) = (1)/(2)x - 3\\g (x) = 3x ^ 2 + x - 6\\(f + g) (x) = f(x) + g (x)\\(f + g) (x) = (1)/(2)x - 3 + 3x ^ 2 + x - 6`

Finally we simplify, and we have left:

`(f + g)(x) = 3x ^ 2 + (3)/(2)x - 9`