INVERSE OF ONE-TO-ONE FUNCTION
- Thread starter achi_kun
- Start date
skeeter
Elite Member
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- Dec 15, 2005
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I assume you want to determine the inverse of the given functions
[MATH]y = \sqrt[5]{x+2} + 2[/MATH]
swap x and y ...
[MATH]x = \sqrt[5]{y+2} + 2[/MATH]
solve for y ...
[MATH]x - 2 = \sqrt[5]{y+2}[/MATH]
[MATH](x - 2)^5 = y+2[/MATH]
[MATH]y = f^{-1}(x) = (x-2)^5 - 2[/MATH]
you try the first one ...
[MATH]y = \sqrt[5]{x+2} + 2[/MATH]
swap x and y ...
[MATH]x = \sqrt[5]{y+2} + 2[/MATH]
solve for y ...
[MATH]x - 2 = \sqrt[5]{y+2}[/MATH]
[MATH](x - 2)^5 = y+2[/MATH]
[MATH]y = f^{-1}(x) = (x-2)^5 - 2[/MATH]
you try the first one ...