# In Linear Algebra, why is $f \circ ( (g+b)(v) = (g+b) \circ ( f(v)$

In linear algebra, assuming I have 3 linear transformations $f,g$ and $b$. Assume that they are all from a space $V$ to the space $V$ (which is finite space). Why is the following true?

$f \circ ( (g+b)(v) = (g+b) \circ ( f(v)$

$v$ being some vector in $V$.

Thanks

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It isn't. Who told you it was? – Robert Israel Feb 3 at 22:50
What is your * operation, since usually a vector space is endowed with a $+$ and scalar multiplication operation, not a full fledged multiplication operation? – Dimitri Surinx Feb 3 at 22:51
I'm sorry, perhaps this wasn't clear. I'm referring to ש Function composition with my * notation – vondip Feb 3 at 22:54
You probably want to use \circ (which produces a $\circ$) for this. – Muphrid Feb 3 at 23:11
Thanks! Just did – vondip Feb 3 at 23:14