$f(\text{b})^\mathcal{M}$
$= f^\mathcal{M}(\text{b}^\mathcal{M})$
$= f^\mathcal{M}(2)$
$= 1$
$f(\text{d})^\mathcal{M}$
$= f^\mathcal{M}(\text{d}^\mathcal{M})$
$= f^\mathcal{M}(4)$
$= 3$
$f\big(f(\text{c})\big)^\mathcal{M}$
$= f^\mathcal{M}\big(f(\text{c})^\mathcal{M}\big)$
$= f^\mathcal{M}\big(f^\mathcal{M}(\text{c}^\mathcal{M})\big)$
$= f^\mathcal{M}\big(f^\mathcal{M}(3)\big)$
$= f^\mathcal{M}(2)$
$= 1$
$f\big(f(\text{b})\big)^\mathcal{M}$
$= f^\mathcal{M}\big(f(\text{b})^\mathcal{M}\big)$
$= f^\mathcal{M}\big(f^\mathcal{M}(\text{b}^\mathcal{M})\big)$
$= f^\mathcal{M}\big(f^\mathcal{M}(2)\big)$
$= f^\mathcal{M}(1)$
$= 4$
$f\big(f\big(f(\text{c})\big)\big)^\mathcal{M}$
$= f^\mathcal{M}\big(f\big(f(\text{c})\big)^\mathcal{M}\big)$
$= f^\mathcal{M}\big(f^\mathcal{M}\big(f(\text{c})^\mathcal{M}\big)\big)$
$= f^\mathcal{M}\big(f^\mathcal{M}\big(f^\mathcal{M}(\text{c}^\mathcal{M})\big)\big)$
$= f^\mathcal{M}\big(f^\mathcal{M}\big(f^\mathcal{M}(3)\big)\big)$
$= f^\mathcal{M}\big(f^\mathcal{M}(2)\big)$
$= f^\mathcal{M}(1)$
$= 4$