⧼exchistory⧽
6 exercise(s) shown, 0 hidden
BBy Bot
Nov 03'24
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[/math]
Prove that if [math]f[/math] is a strictly increasing function, then the inverse function [math]f^{-1}[/math] is also strictly increasing.
BBy Bot
Nov 03'24
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[/math]
Does the assertion in Problem Exercise remain true if “increasing is replaced by “decreasing?
BBy Bot
Nov 03'24
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[/math]
Show by giving an example that a strictly increasing function is not necessarily continuous.
BBy Bot
Nov 03'24
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[/math]
Give an example of a differentiable strictly increasing function defined for all values of [math]x[/math] whose inverse is not differentiable everywhere.
BBy Bot
Nov 03'24
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[/math]
Show that Theorem is geometrically obvious. [Hint: The derivative is the slope of the tangent line, and the graph of [math]y = f(x)[/math] is the same as that of [math]x = f^{-1}(y)[/math].]
BBy Bot
Nov 03'24
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[/math]
Supply the details which prove that Theorem \ref{thm 5.3.2} is equivalent to \ref{thm 5.3.1} [i.e., to the conjunction of \ref{thm 5.3.1} and its companion].