Question 332562
<pre><b>
{{{ f(x)=3x-2}}} and {{{g(x)=x^2-4x+1 }}} find: {{{ (f+g)(x)}}}

(f+g)(x) 

That just means to add together everything written after "f(x)=" and
everything written after "g(x)".

In other words it means the green stuff below PLUS the red stuff below:

{{{f(x)=green(3x-2)}}} {{{g(x)=red(x^2-4x+1) }}}

So put a plus sign between the red and the green stuff:

{{{(f+g)(x)=green(3x-2) + red(x^2-4x+1) }}}

Now you have to simplify.  I'll recolor the terms:

{{{(f+g)(x)=red(3x)-green(2) + x^2-red(4x)+green(1) }}}

Now 

1. Write down the {{{x^2}}} because that's the only
term that has {{{x^2}}}, and also because it has the largest exponent

2. After that combine the red things {{{red(3x)-red(4x)}}}. That gives
{{{(-1x)}}} and you can just write that {{{-x}}}.

3. Finally combine the green things {{{-green(2)+green(1) }}}, getting -1 and you end up with:

{{{(f+g)(x)=x^2-red(x)-green(1) }}}

Didn't take a rocket scientist, did it.  Bet you remember that much
from algebra five years ago.  :-)

Edwin</pre>