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Math Help - What is the purpose of adding functions?

  1. #1
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    What is the purpose of adding functions?

    Hi!
    I know that you can add functions together, like f(x) = 4x+3 and g(x) = 7x-5 and get a new function, h(x) = 11x-2
    Why would someone want to add linear, or quadratic, or whatever functions together? Like are there real world applications for this?
    I know you can add the derivatives of the functions together too, and you get h'(x) = 11. In what case would you want to add the derivatives together?

    Thanks!
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  2. #2
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    Re: What is the purpose of adding functions?

    There are many applications that can be interpreted as a sum of two functions. If, for example, you are standing in an elevator going up at speed v relative to the ground. Your height above the ground is f(t)= vt. You drop a ball which then has distance below your hand g(t)= -gt^2/2. The height of the ball above the ground is f(t)+ g(t)= -gt^2/2+ vt.

    That can also be used the other way. If I have a problem that involves, for whatever reason, the function h(x)= 3x^4+ sin(x) and want to differentiate it, rather than having to memorize a "rule" for differentiating a power of x plus a trig function, I can think of it as the sum of f(x)= 3x^4 and g(x)= sin(x) and differentiate each separately.
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  3. #3
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    Re: What is the purpose of adding functions?

    Consider the relatively simple function

    $f(x) = x^4 - 3x + 2.$

    How do you actually compute it its value for any value of x. You compute $x^4\ and\ then\ -\ 3x + 2$ and add them together.

    In other words, you treat $f(x) = x^4 - 3x + 2\ as\ f(x) = g(x) + h(x),\ where\ g(x) = x^4\ and\ h(x) = - 3x + 2.$

    Yes, you can conceptually view a function as a single entity, but it often is far more useful or practical to view it as being a combination of simpler functions.
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  4. #4
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    Re: What is the purpose of adding functions?

    Later thought

    For a practical example of combining functions for a conceptual (rather than mechanical) purpose outside the realms of natural science, consider the profit function in economics:

    $\pi(p,\ q) = \sigma(p,\ q) - \kappa(q),\ where$

    $\sigma(p,\ q) = sales\ revenue$

    $\kappa(q) = cost\ of\ production$

    $q = quantity\ sold$

    $p = price\ per\ unit\ sold$
    Last edited by JeffM; March 6th 2014 at 09:58 AM.
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