Find the domain and range of the function f(x) = cbrt-x+7.

The function involves a cube root. Unlike square roots, a cube root can take any real number (positive, negative, or zero) as its argument. There are no restrictions on the expression inside a cube root.
Therefore, the expression $-x+7$ can be any real number.
The domain of $f(x)$ is all real numbers.
In interval notation, this is $(-\infty, \infty)$.

Let $y = f(x)$. So, $y = \sqrt[3]{-x+7}$.
To find the range, we can try to express $x$ in terms of $y$:
First, cube both sides of the equation:

Now, solve for $x$:

Since $y^3$ can take any real value (as $y$ can be any real number), the expression $7-y^3$ can also take any real value. This means that for any real value of $y$, there is a corresponding real value of $x$.
Therefore, the range of $f(x)$ is all real numbers.
In interval notation, this is $(-\infty, \infty)$.

The domain of $f(x)$ is $\boxed{(-\infty, \infty)}$.
The range of $f(x)$ is $\boxed{(-\infty, \infty)}$.