# The number of electric scooters e that a factory can produce per day is a function of the number of hours h it operates and is given by e(h) = 290h, 0

The number of electric scooters e that a factory can produce per day is a function of the number of hours h it operates and is given by $e\left(h\right)=290h,0\le h\le 10.$
The daily cost c to manufacture e electric scooters is given by the function $c\left(e\right)=0.05{e}^{2}+65e+1000.$
(a) Find $\left(c\cdot e\right)\left(h\right).$
(b) Evaluate $\left(c\cdot e\right)\left(13\right).$

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The composition of the function c(e) and e(h) is denoted by $\left(c\cdot e\right)\left(h\right)$ is given by the formula,
$\left(c\cdot e\right)\left(h\right)=c\left(e\left(h\right)\right)$
(a) Compute the composite function as,
$e\left(h\right)=290h,0\le h\le 10$
$c\left(e\right)=0.05{e}^{2}+65e+1000$
$\left(c\cdot e\right)\left(h\right)=c\left(e\left(h\right)\right)$
$=c\left(290h\right)$
$=0.05{\left(90h\right)}^{2}+65\left(290h\right)+100$
$3920{h}^{2}+18850h+1000,0\le h\le 10$
(b) The composite function $\left(c\cdot e\right)\left(h\right)$ is not defined for h = 13.
Hence, the function $\left(c\cdot e\right)\left(13\right)$ cannot be evaluated.