# Thread: Expressing x in terms of y

1. ## Expressing x in terms of y

For the function y = f(x) = x^5 + 2x^3 + 3x + 1
How do I go about expressing x in terms of y?
Thanks.

2. Hello tashbo

Welcome to Math Help Forum!
Originally Posted by tashbo
For the function y = f(x) = x^5 + 2x^3 + 3x + 1
How do I go about expressing x in terms of y?
Thanks.
Without wishing to sound frivolous: with great difficulty! The answer is that you may be able to find a value (or possibly several values) of $\displaystyle x$, given a specific value of $\displaystyle y$, but you won't be able to find a formula that will do it for any value of $\displaystyle y$. This is because there's no straightforward way of solving an equation like this - with terms in $\displaystyle x^5,\, x^3$ and $\displaystyle x$.

3. Thanks for that- I think that maybe I am misunderstanding therefore what I need to do!

4. ## Inverse Funtion Rule

how do I find the inverse of f^-1 for a polynomial function such as

y = f(x) = x^5 + 2x^3 + 3x + 1 in order then to go on to use the Inverse Function Rule for some given values?

5. Originally Posted by tashbo
Thanks for that- I think that maybe I am misunderstanding therefore what I need to do!
Originally Posted by tashbo
how do I find the inverse of f^-1 for a polynomial function such as

y = f(x) = x^5 + 2x^3 + 3x + 1 in order then to go on to use the Inverse Function Rule for some given values?

Post the original question! What I've highlighted in red implies crucial missing information - it's almost certain that you don't have to find the rule for the inverse function.

6. It seems that I have repeated myself as I am having difficulty understanding the question I am trying to answer - it was not intentional and I apologise.

Originally Posted by Mr Fantastic
What I've highlighted in red implies crucial missing information - it's almost certain that you don't have to find the rule for the inverse function.
I have to prove that f^-1(7) = 1 and I don't know how to do this without knowing the inverse of the function given.

7. Originally Posted by tashbo
What I've highlighted in red implies crucial missing information - it's almost certain that you don't have to find the rule for the inverse function.
Originally Posted by Mr Fantastic
I have to prove that f^-1(7) = 1 and I don't know how to do this without knowing the inverse of the function given.
*Sigh* By definition: $\displaystyle f(1) = 7 \Rightarrow f^{-1}(7) = 1$.

Life would be so much easier if people just gave the original question instead of censoring it with their bias.