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December 19, 2014

December 19, 2014

Posted by **ayotal** on Wednesday, October 19, 2011 at 6:20pm.

- calculus -
**MathMate**, Wednesday, October 19, 2011 at 11:14pmIn mathematics, you cannot prove that a statement is true by a finite number of examples, because it is not possible to prove all possible cases by a finite number of examples.

However, to prove that a statement is false, you only need ONE counter-example. This is probably your case here.

Try

f(x)=x^2+2,

g(x)=x+2

then fog(x)=f(g(x))=(x+2)^2+2

gof(x)=x^2+4

Since we demonstrated fog(x)≠gof(x), the given statement is not true.

On the other hand, if we define

f(x)=2x, g(x)=4x

then fog(x)=f(4x)=8x^2

gof(x)=g(2x)=8x^2

so fog(x)=gof(x) in this case, BUT it does not prove anything.

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