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I have defined the following function in Mathematica 

al[z_] := (a/((1 + a*(b/(2 Pi))*Log[z/Mz])))

(a and b are defined constants) Now I want to put in a variable x that I will integrate over from 0 to 100, but for low values of x (up to 3) I want the function al to be fixed, i.e., z should be 3 for x < 3 and x for x > 3.

However, I only want this constraint on al when I fill in x. Any ideas on how to do this?

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    $\begingroup$ Why not use Piecewise[], then? $\endgroup$
    – J. M.'s lack of A.I. ♦
    Jul 1, 2016 at 12:11
  • $\begingroup$ Well, I use the function multiple times and if I wanted to fill in a value, say $y$, I did not want that constraint, and trying to be as compact as possible I was wondering whether there was another option. Anyway, thanks. In the end for my specific case the option Min[al[x],al[3]] worked fine as well. $\endgroup$
    – user40834
    Jul 1, 2016 at 16:46

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You could use Clip:

al[ Clip[x, {3, Infinity}] ]
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  • $\begingroup$ Note that this is equivalent to suggestion by @J.M. to use Piecewise. Evaluate Clip[x, {xmin, xmax}] // PiecewiseExpand and Clip[x, {3, Infinity}] // PiecewiseExpand $\endgroup$
    – Bob Hanlon
    Jul 1, 2016 at 15:46
  • $\begingroup$ Cheers, turns out Min[al[x],al[3]] works as well in my particular case $\endgroup$
    – user40834
    Jul 1, 2016 at 16:48

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