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Differentiation
Hi. I have a problem with an AS Level math question on differentiation.
I had to find the inverse of f(x) = 4 - x^2, where x is greater than or equal to 0, which I found to be sq rt (4 - x). However, it then goes on to ask me to show how a solution to f(x) = f^-1(x) can be obtained from x^2 x - 4 = 0. Finding the solution is no problem (1.56), and when I draw the graph I have no problem understanding the connection, but 'showing' the link is causing me to waste reams of paper! As I understand it, I would have to show a link between x^2 x - 4 and 4 - x^2 = sq rt (4 - x), but I come out with x^4 - 8x^2 x 12 = 0 and I just can't catch the link. Again, any help would be most welcome. Thanks. Adrian |
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