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One of the questions assigned to me for homework was:

Is it true that $ f\circ (g \circ h ) =f \circ g + f \circ h$?

I am in the understanding that $f \circ g$ means $f(g(x))$, so $ f\circ (g \circ h )$ is $f(g(h(x)))$.

Well let us take $f(x)=c$ for some constant $c \neq 0$, then $ f\circ (g \circ h ) =f \circ g + f \circ h$, would state that $c=2c \Rightarrow 1=2$, which is obviously false. Is this question really this simple or (which I presume) am I wrong with the definitions ?

Jori
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  • Not true in general, as you pointed out. – parsiad Sep 08 '14 at 16:21
  • You are right in your definition (that $f\circ g = f(g(x))$) and your counter-example is also good (but you might want to add "which is obviously false for $c\not= 0$"). Pat yourself on the back and go find a new problem to solve:) – Winther Sep 08 '14 at 16:26
  • Oops. Yes of course. Thanks. I don't know why they put this question in the homework. The other questions aren't that simple. – Jori Sep 08 '14 at 16:31

1 Answers1

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You were asked to either prove or disprove the statement you were given.

You found a counter example to the statement.

A counter example is a perfectly valid way to disprove a statement. You are done, the statement is false.

Alice Ryhl
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