Question

I am really bad at Domains.
Let f be the function defined by f(x)=(squareroot)x+1/x
a) what is the domain of f

Answer 1

Well, I'm not sure if that's
$$ f(x) = \sqrt{x + \frac{1}{x}} $$or
$$ f(x) = \sqrt{x} + \frac{1}{x} $$
However, the rules of domain are pretty simple. the value of 'x' must not cause an undefined behavior.
For example, x cannot be 0 here because it will cause a division by zero which is undefined.
Also, unless you work with complex numbers, you cannot root a negative number because there is no 'real number' which if you'd square would result in a negative number.
In our case it means x cannot be negative, because in both the equations I wrote above it will cause a root of a negative number.
So we end up with \(x \gt 0\) as the domain of the function.

Answer 2

I wrote root instead square root, sorry.
You cannot square root negative number without using complex numbers.