Why use f(x)?Date: 02/14/99 at 22:27:02 From: ed brown Subject: Why use f(x)? Can you explain the point of using f(x) in an equation as opposed to y? Thanks in advance. Date: 02/15/99 at 08:42:50 From: Doctor Jerry Subject: Re: Why use f(x)? One can use the notation y = x^2-5x+6 for many purposes. The equation can carry the idea that as x changes, y changes. It doesn't give, explicitly, the name of the rule that says that to the number x corresponds the number x^2-5x+6. When we write y = sin(x), we are being redundant, for some purposes. "sin" is the name of a particular rule. Out of habit, we may say "graph the equation y = sin(x)." We could say: graph the function sin. I expect that you also use log or ln, tan, cos, and maybe sqrt(x). Mathematicians often like to be minimalists. If they have a certain rule of correspondence in mind, they may prefer naming it by a letter, such as f. They don't need y = f(x); just f will do. When we want to put two functions together, like ln(sin(x)), we can name the new function as ln o sin. Of course, this can also be done, as you may prefer, by saying something like Y = ln(w) w = sin(x), so, y = ln(sin(x)). Another reason is that calculus is the study of functions, not equations. We study functions f and their derivatives f'. We integrate functions. All of this is possible with the y = x^2+5x+6 notation, but somewhat more awkward, and it takes more talking to be precise. Finally, if f(x) = x^2 and we want to calculate (as is needed in calculus) the difference quotient (this is the slope of the line joining (x,f(x)) and (x+h,f(x+h))) [f(x+h)-f(x)]/h, how could you easily give the recipe using the y = x^2 notation? - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ |
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