Find inverse of function?

Question

OKay, the function is y=x^3+2x-1
Please show all steps that you took to find the inverse.

Answer 1

The derivative of that function is 3x^2+2 which yields a positive number for each x. Therefore the function is always increasing and therefore it IS one-to-one and hence has an inverse. Now what that inverse is, is rather difficult to express. You can write
x^3+2x-1-y=0
and try to solve for x, treating y as a number. For this you may want to take a look at the methid to solve cubic equations. Here is the link to the wikipedia article
http://en.wikipedia.org/wiki/Cubic_equations

However this method is cumbersome and and is algebraically complicated. So instead, if you are just interested in a power series solution around a point, you should look at the practical applications of the inverse function theorem. This is also a good idea if you are only interested in an approximate solution. Here is a starting point for you:

http://en.wikipedia.org/wiki/Inverse_function_theorem

And a final note, if this is a homework problem for a calculus class, then probably you should check that you wrote it down correctly and look into your notes to see if there is a shortcut somehow as it is too complicated for basic tools of calculus. Also, does the question really ask for the inverse or for example the graph of the inverse? Because to get that kind of information for the inverse, you really don't need a formula for the inverse.

Answer 2

y=x for a inverse relation deliver you turn y<=> x ie reflect the function interior the line y=x define the relation deliver f (g) = g(f) for strict inverse function you ought to limit the domain names and stages of the two kin f & g such that f & g are applications you may now define the invertible function. seem up the definition of a function and you will see this is rather trivial. degenerate case the x axis (function) invert, the y axis (no longer and not in any respect a function) this is generalized

Answer 3

x=y^3+2y+1

Solve for y in terms of x - there is your inverse.

The above function in the question is one-to-one because there is a value for y for every value of x.

The poster's suggestion of the inverse function theorem is too cumbersome to be applied to this cubic problem. Such a theorem is first mentioned in graduate level math courses and not Calc 101.

Answer 4

There is no inverse for that funcion, it isn't one-to-one.