Kenneth S. answered • 01/29/17
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Let's cut to the chase: I know this subject & how to teach YOU
1. function has inverse if and only if its graph passes the HORIZONTAL LINE TEST
2. the technique for finding inverse is stated simply as
If y = an expression involving x,
rewrite it as x = an expression involving y, i.e. INTERCHANGE letters x & y in the original statement,
then solve for y, and finally re-label it as f-1.
There are numerous examples of how to do this in textbooks and on this and other websites...
Kenneth S.
MARK M, it is NOT true that all functions have inverses. Only functions that are strictly increasing or strictly decreasing (and which consequently pass the Horizontal Line Test for invertibility) have inverses.
The simple f(x) = x squared does not have an inverse; it's a function because it passes the VERTICAL line test, but it fails the Horizontal Line Test.
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01/29/17
Mark M.
01/29/17