Because of the term $x^{3\/4}$, the interval $\left(-\infty \,0\right)$ is excluded from the domain of $F$.

The graph of $F$ in Figure 1.6.5(a) shows the vertical asymptote whose equation is $x\=\stackrel{\^}{x}\doteq 0.6400732558$ and the horizontal asymptote $y\=\tan \left(4\right)\doteq 1.157821282$.

Thus, $F$ is continuous on $\left(-\infty \,\stackrel{\^}{x}\right)\bigcup \left(\stackrel{\^}{x}\,\infty \right)$.

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

Expression palette: Limit operator
Context Panel: Evaluate and Display Inline

Context Panel: Approximate≻10

Figure 1.6.5(b) is a graph of $g\left(x\right)$ along with the lines $y\=k \mathrm{\π}\/2\,k\=1\,3\,5$. The vertical asymptotes for $\tan \left(x\right)$ occur at the odd half-multiples of $\mathrm{\π}$, so Figure 1.6.5(b) is drawn to see where $g\left(x\right)$, the argument of $\tan \left(g\left(x\right)\right)$, assumes one of these values. The only one is $3 \mathrm{\π}\/2$.

It is also useful to know that $g\left(0\right)$ = $7$, and that the minimum of $g\left(x\right)$ is approximately $3.45$, found by applying the Optimization≻Minimize option from the Context Panel:

Write the equation $g\left(x\right)\=3 \mathrm{\π}\/2$
Context Panel: Solve≻Numerically Solve