What are Domain and Range?
Students are often confused about domain and range of a function. Let's consider the list of points: {(1, 2), (3, 5), (6, 1), (4, 9), (3, 3)}.
The domain is all the xvalues, and the range is all the yvalues. Domain is: {1, 2, 6, 4, 3} Range is: {2, 5, 1, 9, 3} Problem:
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An inverse function is quite simple: it is tells you how to get back to the original value. Another way of looking is that an inverse function is just undoing what was done before. For example, if tied your shoes and then untied them, you used an inverse function to untie them! Another example is when a computer reads a number you type in and converts it to binary for internal storage, then prints it out again as a number on the screen for you to see, it's doing an inverse function.
Example: You are traveling at 70 mph and want to know how far you have gone in x hours. You can use a function to represent it. So, f(x) = 60. x
If you want to know the inverse, that is, if you know you have travelled x miles, and you want to know how long you have been traveling for, you use an inverse function.
\[f^{1}(x) = \frac{x}{60}\]
Problems
1. Find the inverse function of f given by f(x) = 2x + 3
2. Find the inverse function of f given by f(x) = ln(x + 2)  3

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