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How would you solve this exercise?

Determine the values of $\color{teal}a$ for which the following functions: $$\color{maroon}{f:(0,\infty)\to \mathbb{R}},\quad \color{violet} {f(x)=\ln x}$$ and $$\color{maroon}{g:\mathbb{R}\setminus \{0\}\to \mathbb{R} },\quad\color{violet}{g(x)={a\over x}}$$

have one common point.

Thank you very much!

Siminore
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wonderingdev
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1 Answers1

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I would first sketch the graphs of both $f$ and $g$, and then I'd probably justify my answer by the IVT. The case $a>0$ is really simple (just look at the limits as $x \to 0+$ and $x \to +\infty$). The case $a<0$ requires more work.

Siminore
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