Discovery of The Inverse Trig Functions
Does every function have an inverse?
No
Yes
Must the inverse of a function be a function?
Yes
No
How do we know if the inverse of a function, f(x), is also a function?
The graph of f(x) must pass the vertical line test
The graph of f(x) must pass the horizontal line test
What measures can we take, if any, to turn an inverse relation into an inverse function?
We can restrict the domain and/or the range of the relation.
Discovery of the Arcsine Function
What is an appropriate domain for [i]f[/i] or a range for [math]f^{-1}[/math] that would guarantee one output for every input?
Discovery of the Arccosine Function
What is an appropriate domain for [i]f[/i] or a range for [math]f^{-1}[/math] that would guarantee one output for every input?
What is an appropriate domain for [i]f[/i] or a range for [math]f^{-1}[/math] that would guarantee one output for every input?
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Information: Discovery of The Inverse Trig Functions