Calculate the inverse of f(x) = x^3 = 3x^2 + 3x -1

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In summary, the conversation discusses finding the inverse of the function f(x) = x^3 - 3x^2 + 3x - 1. One suggestion is to use polynomial long division to divide by a value x0 that makes f(x) = 0. Another suggestion is to use Pascal's Triangle to factor the function and find the inverse. The conversation also mentions the coefficients of the function and their interesting pattern.
  • #1
mooneh
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f inverse for f(x)= x^3-3x^2+3x-1

i thought of taking x common factor x(x^2-3x+3)-1
but i got stuck with the quadratic equation !
HELP...
 
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  • #2
The coefficients of x^3, x^2, x, and 1 are +1, -3, +3, -1, an interesting pattern. Can you guess a value of x that makes f(x)=0 ? Call that value x0. Then, you can divide f(x) by x-x0 using polynomial long division: http://www.purplemath.com/modules/polydiv2.htm. That will give you a quadratic that you can factorize.
 
  • #3
better yet to factorise...from x^3-3x^2 is there any factor you can't take out to make it 3x-1?
 
  • #4
Sorry!, please note that the rules for the Homework Help forums explicitly state that full answers should never be given to students.
 
  • #5
ooooh my bad. sorry about that cristo... i never saw a post about rules :eek:

but yeah... mooneh have you ever used or heard of Pascals Triangle before it's much easier to factor than long/synthetic division etc. etc. especially for the particular function you stated... from there you just solve to get the inverse
 
Last edited:

1. How do I calculate the inverse of a function?

To calculate the inverse of a function, you need to switch the positions of the x and y variables and solve for the new y variable. This will give you the inverse function, which is denoted as f^-1(x).

2. What is the inverse of f(x) = x^3?

The inverse of f(x) = x^3 is f^-1(x) = cubed root of x.

3. What are the steps for finding the inverse of a cubic function?

The steps for finding the inverse of a cubic function are:

  1. Switch the x and y variables in the original function.
  2. Solve for y in terms of x.
  3. Replace y with f^-1(x) to get the inverse function.

4. How do I graph the inverse of a cubic function?

To graph the inverse of a cubic function, plot the points of the inverse function by switching the x and y coordinates of the original points. Then, connect these points to create the inverse function graph.

5. Can every function have an inverse?

No, not every function has an inverse. A function must be one-to-one, meaning each x value has a unique y value, in order to have an inverse. Cubic functions are one-to-one and therefore have an inverse, while functions like f(x) = x^2 are not one-to-one and do not have an inverse.

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