Generating inverse

Mar 2017
358
3
Massachusetts
Can someone help me find the inverse of $y = 7 + 5x^3 + x^7$? The fact that there is more than one variable to a unique power makes the inverse a little less obvious than usual.
 

romsek

MHF Helper
Nov 2013
6,838
3,079
California
What makes you think there exists a closed formula for this inverse function?
 

Plato

MHF Helper
Aug 2006
22,507
8,664
Can someone help me find the inverse of $y = 7 + 5x^3 + x^7$? The fact that there is more than one variable to a unique power makes the inverse a little less obvious than usual.
Did you look at the PLOT of this function?
Does it have an inverse?
 
Mar 2017
358
3
Massachusetts
ah...that's a fair point you made. What if you restricted the domain to [-1.21, 1.21], then what would be its inverse ?
 
Dec 2016
315
171
Earth
Did you look at the PLOT of this function?
Does it have an inverse?
It's entered correctly in the quote box of post # 4, but some
other expression was entered at the link for the graph.

- - - - - - - - - - - - - - - - - -

otownsend, no restrictions have to be made on the domain.
But as romsek's post questioned about it, it does not
have a closed form.
 
Last edited:
Dec 2014
166
126
USA
Is there more to this problem that you haven't posted, say, finding the value of the derivative of the function's inverse at a specific value?