本题目来源于试卷: Trigonometric Functions，类别为 IB数学
[问答题]
Consider the function defined by akexg a.c6/a a f.q,2l:/g4 klp*r nh lz5j+wz $f(x)=\frac{7}{x^{2}+6 x-7}$ for $x \in \mathbb{R}$,$ x \neq-7$,$x \neq 1$ .
1. Sketch the graph of y=f(x) , showing the values of any axes intercepts, the coordinates of any local maxima and minima, and the graphs of any asymptotes.
Next, consider the function g defined by $g(x)=\frac{7}{x^{2}+6 x-7}$ for $x \in \mathbb{R}$, x>1 .
2. Show that $ g^{-1}(x)=-3+\sqrt{\frac{16 x+7}{x}}$ .
3. State the domain of $g^{-1}$ .
Now, consider the function h defined by $h(x)=\arccos \left(\frac{x}{7}\right)$ .
4. Given that $(h \circ g)(a)=\frac{\pi}{3}$ , find the value of a . Give your answer in the form $ p+q \sqrt{2}$ where p, q$\in \mathbb{Z}$ .
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