Expressing x in terms of y

**tashbo** · August 18th 2009, 04:24 AM

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

**Grandad** · August 18th 2009, 04:58 AM

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 $x$ , given a specific value of $y$ , but you won't be able to find a formula that will do it for any value of $y$ . This is because there's no straightforward way of solving an equation like this - with terms in $x^5,\, x^3$ and $x$ .

Grandad

**tashbo** · August 18th 2009, 05:20 AM

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

**tashbo** · August 18th 2009, 06:14 AM

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?

**mr fantastic** · August 18th 2009, 06:37 AM

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?

This is essentially the same question that you've already asked. The reply given by Grandad still applies.

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.

**tashbo** · August 18th 2009, 07:23 AM

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.

**mr fantastic** · August 18th 2009, 07:29 AM

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: $f(1) = 7 \Rightarrow f^{-1}(7) = 1$ .

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

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