Find the inverse of h(x)=x+sqrt x

Question

kkutie7 · Answer

lets work through this in steps shall we? =)

mathmale · Answer

Please note:$$y=x+x^{\frac{1}{2}} \neq x^{\frac{3}{2}}$$

kkutie7 · Answer

I messed up let me fix that!

mathmale · Answer

@Theanitrix :  Could you please become involved?   Thanks.

anonymous · Answer

Yeah, I had tried that approach but I realized it wasnt valid

anonymous · Answer

The full question is to find h^-1(6), which is 4

anonymous · Answer

but I the only reason I found that answer was because I set 0=x+sqrt x

anonymous · Answer

I want to find the more general answer, which would be the inverse of the function

anonymous · Answer

sorry I meant * 6= x+ sqrt x

mathmale · Answer

Find the inverse of h(x)=x+sqrt x
Replace that h(x) with "y="
Interchange x and y; where you see x, write y; where you see y, write x

mathmale · Answer

Solve the resulting equation for y.

anonymous · Answer

Yeah I know the steps, but my equation is not correct when I do it

anonymous · Answer

Give me a sec to try it again

mathmale · Answer

You state:  "The full question is to find h^-1(6), which is 4 "      This is equivalent to saying that h(4)=6.  It so happens that 
$$h(x)=x+x ^{1/2}$$

mathmale · Answer

becomes, when x=4, $$h(4)=4+4^{1/2}=4+2=6, $$

... which is what we expected.

In summary, if h(4) = 6, then $$h ^{-1}(6)=4.$$

mathmale · Answer

If y ou want a truly general solution, you'll have to go through those "steps" you and I both mentioned earlier.

anonymous · Answer

ah okay I see, I figured. Thank you, I'll see if I can work through those "steps"