## Change in variables

1. The problem statement, all variables and given/known data
I am performing a change of variables, s --> t and am wondering can I just write g(s) --> g(t) or do I have to alter the function e.g. g(s) --> a*g(t).

2. Relevant equations
s = (a/b)* t
g(s) is to be found numerically and therefore we do not have it's definition.

So Option one:
just rewrite g(s) as g(t)

Option two:
g(s) = (a/b)*g(t)

Thanks

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 Um, generally, if s -> t, then g(s) does NOT go to g(t). If you know that g is continuous, then you may assume that. Otherwise, you will have to work off the official definition of limits.
 I would assume that if s => ta /b, g(s) => g(ta/b) if a,b are arbitrary / real constants. I could be wrong though.

## Change in variables

That's definitely not true. Consider the function

g(x) = x + 1 for x > 0 and x - 1 for x <= 0. Then as s -> 0 from the right, g(x) => 1, even though g(0) = -1.

Recognitions:
Gold Member
MathMonster, there are times when that is acceptable but I would avoid it. Technically if, for example, $f(s)= s^2- 3s+ 2$ then $f(t)= t^2- 3t+ 2$ but I don't believe that is what you are trying to do. If [itex]f(s)= s^2- 3s+ 2[/tex] then replacing s with t= s-2 gives, since s= t+2, [itex]f(s)= f(t+ 2)= (t+ 2)^2- 3(t+ 2)+ 2= t^2+ 4t+ 4- 3t- 6+ 2= t^2+ t[/tex] but notice that is f(t+2), not f(t). If you like you say explicitely that g(t)= f(t+ 2) and then use g(t).