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

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

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

Is it even possible to find the inverse of this?

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

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

3. 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 $\displaystyle x=y+\sqrt{y}$
*edit* the question is find $\displaystyle f^{-1} (6)$ but to do that I must 1st find $\displaystyle f^{-1} (x)$

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

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

Just by looking I can see the answer is 4

$\displaystyle 6=x+\sqrt{x}$

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