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3 problems match “exponential functions”. Clear

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1. Value of an odd function ●○○○○ 10 ptsThe function $y=f(x)$ is an odd function, and $f(x)=3^x - 1$ for $x \geq 0$. Find $f(-2)$.
2. Finding a from two points on a graph ●●●○○ 50 ptsGiven a constant $a > 0$, the graph of the function $f(x)= \frac{2^{x}}{2^{x}+ax}$ passes through the points $P\left(p, \frac{6}{5}\right)$ and $Q\left(q, -\frac{1}{5}\right)$. If $2^{p+q}=36pq$, find the value of $a$.
3. Maximum integer k in a derivative inequality ●●●●○ 100 ptsLet $f(x)=e^{x}-x-2$. For $x>0$, the inequality $(x-k)f'(x)+x+1>0$ always holds, where $k$ is an integer. Find the maximum value of $k$.