Question

9" id="TexFormula1" title="f(x)=|3x-5|+7x\\g(x)=-2x+9\\what is \\ (f+g)(x)" alt="f(x)=|3x-5|+7x\\g(x)=-2x+9\\what is \\ (f+g)(x)" align="absmiddle" class="latex-formula">

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