Control-drag (or type)  $f\left(x\right)\=\dots$ 
Context Panel: Assign Function

The graph of $f$ in Figure 1.6.2(a) suggests its domain is the closed interval $\left[3\,7\right]$, the set of points for which $10 x-x^2-21\ge 0$.

The endpoints: $f\left(x\right)\=0$$\stackrel{\text{solve}}{\to }$$\left\{x\=3\right\}\,\left\{x\=7\right\}$ 

The domain $3\le x\le 7$ can be inferred from:
 $f\left(x\right)$ = $\sqrt{10x-x^2-21}$$\stackrel{\text{factor}}{\=}$$\sqrt{-\left(x-3\right)\left(x-7\right)}$

Alternatively, form an inequality in which the radicand is to be nonnegative.

Context Panel: Solve≻Solve

The function value at $x\=3$ agrees with the limit from the right at $x\=3$. Hence, $f$ is continuous from the right at $x\=3$.

The function value at $x\=7$ agrees with the limit from the left at $x\=7$. Hence, $f$ is continuous from the left at $x\=7$.