Question 204173: what does g(x) and f(x) mean and what purpose do they serve?
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! if we use,,y=2x,,,this is well defined, on a x-y coordinate plane, y rises twice as fast as x moves to right.
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g(x) =2x or h(x) =2x,,,,,mean the same thing,,,except the axis is now g(x),,or h(x).
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The advantage of using functional notation is that different items can be differentiated, and still shown to be a function of x.
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If we had a cost, we might use c(x). If we just used "c", it might not be clear that it is a function of x.
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Some problems have multiple functional relationships, we could use y(1), y(2), and y(3), ( and then use a let y(1) = cost, y(2) = quantity, etc), but it might be easier to just use c(x), q(x), t(x), etc to differentiate.
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The composite functions of higher math often use h(x) and g(x), in combination,,defining which comes first, and which is second. The substitution is bad enough, but using y's would make it worse.
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In summary, feel free to immediately use "y =" instead of "h(x)",
if it clarified the problem.
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