Math Tutoring on Inverse Trigonometric Functions
If ‘f’ is a function from a Set A to a Set B, then an Inverse Function for ‘f’ is a function from B to A, with the property that a round trip (a composition) from A to B to a (or B to A to B) returns each element of the initial set to itself.
Thus, if an input ‘x’ into the function ‘f’ produces an output ‘y’, then inputting ‘y’ into the Inverse Function produces the output ‘x’ and vice versa.
A function ‘f’ that has an Inverse is called Invertible; the Inverse Function is then uniquely determined by ‘f’ and is denoted by ‘.
Some important points to determine an Inverse Function:
1. Determine if the function is one-to-one.
2. Interchanging the ‘x’ and ‘y’ variables. This new function is the Inverse Function.
3. If the result is an equation, solve the equation for ‘y’. Replace ‘y’ with the ‘’, symbolizing the Inverse Function or the Inverse of ‘f’.
4. The Domain of ‘f’ is the Range of and the Range of ‘f’ is the Domain of ‘’.
5. The graphs of ‘f’ and ‘’ are reflections of each other across the line y=x.
We could perform this procedure on any function in math tutoring, but the resulting inverse will only be another function if the original function is One-To-One. To determine the Inverse of the Trigonometric Functions, we have to restrict the Domain of a function to make it one-to-one, without changing the Range.
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1. Give the definition of Inverse Function?
2. What are the requisites of an Inverse Function?
3. How can we determine the Inverse of Trigonometric Functions?
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