8b3e47…: “Far from the windless disk”

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Select True if the statement is always true; otherwise, select False.

Let $f$ be a one-to-one function and $f^{-1}$ its inverse. If the point $(2,5)$ lies on the graph of $f$, then the point $(5,2)$ lies on the graph of $f^{-1}$.

True False

The graph of $f$ contains all points of the form $\left (a,f(a)\right )$ whereas the graph of $f^{-1}$ contains all points of the form $\left (f(a),f^{-1}(f(a))\right )=(f(a),a)$.

\[ \sin ^{-1}(\pi ) = 0 \]

True false

The range of $\sin $ is $\left [-1,1\right ]$ and so the domain of $\sin ^{-1}$ is $\left [-1,1\right ]$. We see then than $\pi $ is not in the domain of $\sin ^{-1}$ so $\sin ^{-1}(\pi )$ does not exist.