How do you find the domain of #f(x)=sqrt(1/2x-10)+3#?
The domain is
The domain is determined of what's under the square root sign.
Therefore the domain of
The domain of a real function of real variable is the subset of the real numbers formed by those numbers for which the image exists:
This assumes, in order to obtain the domain of the function, that when a function's formula only contains internal operations in
The square root is a non-internal operation in
So to know when the radicand is positive or negative, what we do is equate to zero:
and then we can define the domain of
To solve the domain of the function above:
we must equal zero the term inside the root:
and solve the equation obtained:
It is easy to see that if