$C=\frac{7x}{100-x}$

$($a$)$ What is the implied domain of C$?($Enter your answer using interval notation.$)$

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Explain your reasoning.

The function is defined for all $x-$values except $x=100.$

You cannot remove $0\%$ of the pollutants.

Negative $x-$values and values greater than $100$ do not make sense in this context. $\frac{A}{s}o,C(100)$ is undefined.

Since we are removing poth, ants, only negative x$-$values make sense in this context.

It would be cost prohibitive to remove more than sow of the pollutants.