F(x)=|3x-5|+7x\\g(x)=-2x+9\\what is \\ (f+g)(x)

Question

`f(x)=|3x-5|+7x\\g(x)=-2x+9\\what is \\ (f+g)(x)`

Answer 1

Given:

The functions are:

`f(x)=|3x-5|+7x`

`g(x)=-2x+9`

To find:

The function
`(f+g)(x)`.

Solution:

We have,

`f(x)=|3x-5|+7x`

`g(x)=-2x+9`

We know that,

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

On substituting the values of given functions, we get

`(f+g)(x)=|3x-5|+7x+(-2x+9)`

`(f+g)(x)=|3x-5|+7x-2x+9`

`(f+g)(x)=|3x-5|+5x+9`

Therefore, the required function is
`(f+g)(x)=|3x-5|+5x+9`.