Let f : R → R be defined by f (x) = 1/x ∀ x ∈ R. Then f is

The correct option is "f is not defined".

To understand why this is the correct choice, let us analyze the definition of a function and the domain given in the problem.
A function $f:A\to B$ is a relation that assigns to each element $x$ in the domain set $A$ exactly one element $y$ in the codomain set $B$. For the function to be well-defined, $f\left(x\right)$ must be a real number for every $x$ in the domain $A$.

Here, the function is defined as:
$f:ℝ\to ℝ$ given by $f\left(x\right)=\frac{1}{x}$ for all $x\in ℝ$.

The domain of the function is specified as the set of all real numbers, $ℝ$. This set includes the number $0$ (zero).
Let us evaluate the function at $x=0$:
$f\left(0\right)=\frac{1}{0}$

Division by zero is undefined in the set of real numbers. Therefore, $f\left(0\right)$ does not exist (is not a real number).
Since there exists an element in the domain (namely, $x=0$) for which the function value is not defined, the rule $f\left(x\right)=\frac{1}{x}$ does not qualify as a valid function from $ℝ$ to $ℝ$.
Thus, the function $f$ is not defined on the given domain.