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[tex]f(x) = 1 - \frac{x^2}{4} , -2 \leq x \leq 2 [/tex]

in terms of Legendre polynomials.

I know that the transformation

[tex]u = \frac{x}{2}[/tex]

maps the function onto the interval (-1,1), but how do I apply this transformation?

Should I use

[tex]g(x) = uf(x)[/tex]

or maybe

[tex]g(x) = f(u(x))[/tex]

?