Solve y =(4th root of x) +1

I have graphed this function and can see that there are no real solutions for x. I would draw the graph here but don't know how to. It starts off at (0,1) and the x value increases rapidly as the y value increases slowly.

But then I tried to solve for x using algebra and found a real solution.

See below:

Let 0=(4th root of x) +1

-1=(4th root of x)

(-1)^4 = (4th root of x)^4

1 = x

So I have a solution of x =1 and yet the function does not cross the x axis at any point when I graph it.

Is someone able to show me why there is no solution on the graph but there is one when I use algebra. I am assuming that my algebra is wrong somewhere but can't see where.

Thanks a lot.

Zen

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