# Thread: How to find inverse of polynomial equation?

1. ## How to find inverse of polynomial equation?

Problem:
f(x) = x^3 + x + 1

Question:
What is f^-1(x)? What is f^-1(0.5)?

How would we change this equation into it's inverse? Do we solve for x such as this?

y = x^3 + x + 1
y - 1 = x(x^2 + 1)

2. Originally Posted by florx
Problem:
f(x) = x^3 + x + 1

Question:
What is f^-1(x)? What is f^-1(0.5)?

How would we change this equation into it's inverse? Do we solve for x such as this?

y = x^3 + x + 1
y - 1 = x(x^2 + 1)
swap x and y in your function and then convert the equation in terms of y

that is,

write $y = x^3+x+1$ as

$x = y^3+y+1$ .

3. Originally Posted by harish21
swap x and y in your function and then convert the equation in terms of y
Of course, but how with a cubic? complete the cube?

4. Originally Posted by pickslides
Of course, but how with a cubic? complete the cube?
Cubic function! now thats troublesome..

5. Well the answer they got in the back is -0.424 for the inverse of f(x).

So would we have to factor out that x^3 + x?

6. Originally Posted by florx
Well the answer they got in the back is -0.424 for the inverse of f(x).

So would we have to factor out that x^3 + x?
Check if your question really is $y = x^3+x+1$. The inverse of this cubic function would look like this:

inverse

7. Holy smokes that is a lot of work. Anyways I am pretty sure that is what they are asking for.

Here is a scan of the question.

8. Originally Posted by florx
Holy smokes that is a lot of work. Anyways I am pretty sure that is what they are asking for.

Here is a scan of the question.

I don't see "What is f^-1(x)?" asked in this attachment. Next time give the actual question, not your (incorrect) interpretation of the question.

Let $f^{-1}(1/2) = a$.

Since (1/2, a) is a point on the graph of $y = f^{-1}(x)$ it follows that (a, 1/2) is a point on y = f(x).

Therefore $\frac{1}{2} = a^3 + a + 1 \Rightarrow a^3 + a + \frac{1}{2} = 0$ and you're expected to use technology to solve this equation.

9. Sorry but I am not familiar with solving cubic polynomials. How would we solve a^3 + a + 0.5 = 0? Do we move the 0.5 to the right side and factor out the a?

Such as a(a^2 + 1) = -0.5?

10. Originally Posted by florx
Sorry but I am not familiar with solving cubic polynomials. How would we solve a^3 + a + 0.5 = 0? Do we move the 0.5 to the right side and factor out the a?

Such as a(a^2 + 1) = -0.5?
*Ahem*:

Originally Posted by mr fantastic
[snip]
and you're expected to use technology to solve this equation.

11. I know that but my teacher is strict about showing work on homework.

12. Originally Posted by florx
I know that but my teacher is strict about showing work on homework.
Then you should ask your teacher how s/he intends you to solve the cubic equation that arises from this question ....

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# f inverse of a cubic equation

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