How to find the inverse of f(x)=x+sqrt(x)?

**yoman360** · October 29th 2009, 08:06 PM

$f(x)=x+\sqrt{x}$

Is it even possible to find the inverse of this?

*edit* the question is find $f^{-1} (6)$ but to do that I must 1st find $f^{-1} (x)$

**artvandalay11** · October 29th 2009, 08:10 PM

it is possible, but rather pointless for this exercise, you just say $x=y+\sqrt{y}$

**yoman360** · October 29th 2009, 08:15 PM

Originally Posted by artvandalay11

when you say is it possible i believe you're talking about elementary operations and as far as i know, you can't solve for that inverse algebraically in terms of y, you just say $x=y+\sqrt{y}$

*edit* the question is find $f^{-1} (6)$ but to do that I must 1st find $f^{-1} (x)$

**artvandalay11** · October 29th 2009, 08:34 PM

no, you just need to find what value of x gives 6 as an answer,

when they say find $f^{-1}(6)$ they are asking what value of x gives 6 as an output for f(x), and you do not need a formula for $f^{-1}$

Just by looking I can see the answer is 4

$6=x+\sqrt{x}$

**HallsofIvy** · October 30th 2009, 04:20 AM

Yes, x= 4 works. And that is as good a method as any!

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