Question

F(x)=2x+3 and g(x)=x^2-8, find (f+g)(x)

Answer 1

`(f+g)(x)=x^2+2x-5`

Explanation:

Given:

The functions given are:

`f(x)=2x+3\\g(x)=x^2-8`

To find:
`(f+g)(x)`

`(f+g)(x)` is equal to the addition of both the functions. So, we need to add the values of both the functions and then simplify to arrive the final answer.

Therefore,
`(f+g)(x)` is given as:

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

Plug in the values of
`f(x)\ and\ g(x)` and simplify. This gives,

`(f+g)(x)=2x+3+x^2-8`

Combining like terms using commutative property of addition, we get

`(f+g)(x)=x^2+2x+3-8\\(f+g)(x)=x^2+2x-5`

Therefore, the addition of the two functions is simplified to:

`(f+g)(x)=x^2+2x-5`