Functional Programming and Math, What you need to know

Functional programming can be better understood if one understands functional composition concepts that are often taught in precalculus and college algebra. A mathematical functional composition problem requires at least two functions. In a two function problem, the result obtained from evaluating one function is substituted into the dependent variable of another function to obtain the final output. 

For example,  given the two functions

f(x) = x + 2 

g(x) = 3x 

find the composition of g(f(2)) means to first evaluate f(2) and then substitute that value into x of g(x) to obtain the final result. 

Since f(2) = 2 + 2 = 4

Substituting 4 into x in the g(x) equation yields

g(4) = 3*4 = 12 

so g(f(2)) = 12 

Functional composition can be extended to 3 or as many functions as you like. Simply take the output of the function and feed it into the independent variable of another function. Then take that output and feed it into another function. 

Functional programming works along the same math based mindset. Functional programming takes an output of a function, such as a JavaScript function and feeds it  into another function You can chain together as many JavaScript functions as you like.  

Other concepts such as recursion also come into play in functional programming. Recursion, is slightly different than functional composition. Instead of feeding the output of the function into the independent variable of another function, you feed the output of one function back into the independent variable of  the same function. 

Posted By: Mark Stansberry, www.bookmarktutorin.com on Sept 18 2014

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