Inverse function

[faadi]

Hello,

Kindly advise how to find inverse of function x³-9x+1=0

 

[Deleted member 4993]

Hello,

Kindly advise how to find inverse of function x³-9x+1=0

What you posted is an equation - not a function. As far as I know, equations do not have inverses.

A function would be written like:

y = x³ - 9x + 1

To invert the function above - you need to first interchange 'x's and 'y's, giving you:

x = y³ - 9y + 1

and so on....

 

[stapel]

Kindly advise how to find inverse of function x³-9x+1=0

Are you supposed to find the inverse of f(x) = x^3 - 9x + 1, or are you supposed to solve x^3 - 9x + 1 = 0? Also, is the power on the leading term really 3, or is it actually 2?

When you reply, please include a clear listing of your efforts so far. Thank you!

 

[lookagain]

Hello,

Kindly advise how to find inverse of function x³-9x+1=0

If f(x) = x³ - 9x + 1, then it has no inverse because it is not one-to-one.

(It doesn't pass the horizontal line test.)


Even if the domain were restricted to [0, oo), it still wouldn't have an inverse,
because the portion of the cubic to the right of the x-axis would not pass the
horizontal line test.

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If it were the case that f(x) = x² - 9x + 1, then it would not have an inverse.

No vertical parabolas pass the horizontal line test.


For this particular hypothetical situation, even if the domain were restricted to [0, oo),
it still wouldn't have an inverse, because the portion of the parabola to the right of the
x-axis would not pass the horizontal line test.