本题目来源于试卷: Exponent-Log Functions，类别为 IB数学
[问答题]
Consider the function dd2zo 2pih9 7) cp)vsvt,z gct.efined by83 fq)mm,6-bgeui f+uroz iu9 $f(x)=(2 x-6) \ln (x+3)+x $ for $x \in \mathbb{R}$, x>p .
1. Find the value of p .
2. Find an expression for $f^{\prime}(x)$ .
The graph of y=f(x) has no points of inflexion.
3. Determine if the graph of y=f(x) is concave down or concave up over its domain.
The function g is defined by $g(x)=3 \ln \left(\frac{1}{x+3}\right)+x$ , for $x \in \mathbb{R}$, x>-3 .
4. Find an expression for $g^{\prime}(x)$ .
5. Find the horizontal and vertical asymptotes of $g^{\prime}(x)$ .
6. Find the exact value of the minimum of y=g(x) .
7. Solve f(x)-3$ .
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