Functions/R/Composition and multiplication/Exercise

Let

$f,g,h\colon \mathbb {R} \longrightarrow \mathbb {R}$

denote functions.

a) Show the equality

${}{\left(h\cdot g\right)}\circ f={\left(h\circ f\right)}\cdot {\left(g\circ f\right)}\,.$

b) Show by an example that the equality

${}{\left(h\circ g\right)}\cdot f={\left(h\cdot f\right)}\circ {\left(g\cdot f\right)}\,$

does not hold in general.

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