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how to generate piecewise function from two lists


Hello

Suppose we have two lists
f={a,b}
r={0,1,2)

In general, the lengths of f and r can vary but the length of f is always 1 less than length of r.

Using the lists f and r, I want to define a piecewise function of the form:

Piecewise[{{a,0<x<1},{b,1<x<2}}] i.e., having the form

Piecewise[{{f[[1]],r[[1]]<x<r[[2]]},{f[[2]],r[[2]]<x<r[[3]]}}]

Is there a way to define a piecewise function using f and r for the general case, as described above.

Thanks

S



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