1. ## Subtracting two functions

I'm trying to figure out how to properly subtract two functions that do not have the same domain. The example that I'm using is attached in this post - where I'm suppose to subtract g from f. While I could estimate the corresponding y-coordinate for g(3), I'm not sure how to find the exact y-coordinate. Any ideas? It appears to be 2.3, but I would prefer not to estimate.

2. ## Re: Subtracting two functions

To subtract functions they need to have the same domains. So you would need to start by restricting the domain for g.

As you do know the exact values for the endpoints of g, you can get the equation of the line and THEN get the value for g(3).

3. ## Re: Subtracting two functions

Originally Posted by otownsend
I'm trying to figure out how to properly subtract two functions that do not have the same domain. The example that I'm using is attached in this post - where I'm suppose to subtract g from f. While I could estimate the corresponding y-coordinate for g(3), I'm not sure how to find the exact y-coordinate. Any ideas? It appears to be 2.3, but I would prefer not to estimate.
It seems the this is a completely standard question.
$f(x)=m_fx+b_f~\&~g(x)=m_gx+b_g$ where $m_g<0<m_f$ are their slopes while $b_f~\&~b_g$ are the $y$-intercepts.

$[f-g](x)=(m_fx+b_f)-(m_gx+b_g)=(m_f-m_g)x+b_f-b_g$

I would not presume to think that we could know with any actuary the values of $m_f,~m_g,~b_f~\&~b_g$.

4. ## Re: Subtracting two functions

If you have two points on a line you can find any point on the line exactly...