Blog: `f(x) = cot(x), (0, pi)` Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

$\displaystyle{f{{\left({x}\right)}}}={\cot{{\left({x}\right)}}},{\left({0},\pi\right)}$ Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

We are asked to determine if the function $\displaystyle{y}={\cot{{\left({x}\right)}}}$ on $\displaystyle{\left({0},\pi\right)}$ has an inverse function by finding if the function is strictly monotonic on the interval using the derivative.

$\displaystyle{y}'=-{{\csc}}^{{2}}{\left({x}\right)}$ . On $\displaystyle{\left({0},\pi\right)},-{{\csc}}^{{2}}{\left({x}\right)}<{0}$ for all x so the function is monotonic and has an inverse function.

We are asked to determine if the function $\displaystyle{y}={\cot{{\left({x}\right)}}}$ on $\displaystyle{\left({0},\pi\right)}$ has an inverse function by finding if the function is strictly monotonic on the interval using the derivative.

$\displaystyle{y}'=-{{\csc}}^{{2}}{\left({x}\right)}$ . On $\displaystyle{\left({0},\pi\right)},-{{\csc}}^{{2}}{\left({x}\right)}<{0}$ for all x so the function is monotonic and has an inverse function.

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$\displaystyle{f{{\left({x}\right)}}}={\cot{{\left({x}\right)}}},{\left({0},\pi\right)}$ Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

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What are the problems with Uganda's government?

Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

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What are the problems with Uganda&#39;s government?

$\displaystyle{f{{\left({x}\right)}}}={\cot{{\left({x}\right)}}},{\left({0},\pi\right)}$ Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

What are the problems with Uganda's government?