Question

If f(x)=x+3 and g(x)=x-3 find (f-g)(x)

Answer 1

`(f-g)(x)`
`=6`

Explanation:

Given:

`f(x)=x+3\\g(x)=x-3`

To find
`(f-g)(x)`

Solution:

In order to find
`(f-g)(x)` we will subtract the function
`g(x)` from
`f(x)`

So, we have:

`(f-g)(x)`
`=f(x)-g(x)`

Plugging in
`f(x)` and
`g(x)` in the above combinations of functions.

`(f-g)(x)`
`=(x+3)-(x-3)`

Simplifying by removing the parenthesis and reversing the signs of the terms in the parenthesis after the negative.

`(f-g)(x)`
`=x+3-x+3`

Combining like terms.

`(f-g)(x)`
`=x-x+3+3`

∴
`(f-g)(x)`
`=6`