First, students will learn that the inverse of an increasing function is also increasing. This can be shown by graphing some functions that students know are monotonic, alongside their inverses. After that, students will learn how to graph an inverse trig function by first finding its domain and range.
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Conclude by giving your students these challenges:
Make the equation below true by replacing each letter with a unique digit (0-9).$$BA = A \times A \times A$$
Here's the solution:
\(A \times A \times A = A^3.\) Thus, \(BA = A^3.\) Hence, \(BA\) is a two-digit cubed number, ending in \(A.\) By listing the first few cubes, we find \(3^3 = 27\) and \(4^3 = 64\) are the only two-digit cubed numbers, and only \(64 = 4^3\) fits \(BA = A^3.\) In conclusion, our equation is \(64 = 4 \times 4 \times 4.\)