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05:15:32 AM May 5th 2011
"if x=y then f(x)=f(y)" -every algebra textbook ever

Isn't that wrong? for example:

f(x)=3x+9 f(y)=1.5y-3

Those two aren't equal at all...
10:02:07 AM May 5th 2011
That's not how that theorem works. Any given function "f" is the same regardless of what's in the parenthesees, and the only thing the letter in the parenthesees indicates is what letter gets used in that function. If f(x) = 3x+9, then f(y) = 3y+9. You can't say f(y) is something different because that would be changing the function "f".

The theorem is that if x = y, then for any given function f, f(x) = f(y).
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