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Q.2 Let $f$ , $g$ and $h$ be functions from $R$ to $R$ . Show that
$\\(f + g) o h = foh + goh\\ (f \cdot g) o h = (foh) \cdot (goh)$

Answers (1)

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To prove : $\\(f + g) o h = foh + goh$

$((f + g) o h)(x)$

$=(f + g) ( h(x) )$

$=f ( h(x) ) +g(h(x))$

$=(f o h)(x) +(goh)(x)$

$=\left \{ (f o h) +(goh) \right \}(x)$ $x\forall R$

Hence, $\\(f + g) o h = foh + goh$

To prove: $(f \cdot g) o h = (foh) \cdot (goh)$

$((f . g) o h)(x)$

$=(f . g) ( h(x) )$

$=f ( h(x) ) . g(h(x))$

$=(f o h)(x) . (goh)(x)$

$=\left \{ (f o h) .(goh) \right \}(x)$ $x\forall R$

$\therefore$ $(f \cdot g) o h = (foh) \cdot (goh)$

Hence, $(f \cdot g) o h = (foh) \cdot (goh)$

Posted by

seema garhwal

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