For $x ∈ R - \{0\}$, the function $f(x) =\frac{3}{x}+ 7$ is decreasing when

$x ∈R-\{0\}$

The correct answer is Option (2) → $x ∈R-\{0\}$

Given $f(x)=\frac{3}{x}+7$ with $x\in\mathbb{R}\setminus\{0\}$.

Derivative:

$f'(x)=-\frac{3}{x^2}$

Since $x^2>0$ for all $x\neq 0$, we have $f'(x)=-\frac{3}{x^2} < 0$ for all $x\neq 0$.

Conclusion: The function is decreasing for all $x\in\mathbb{R}\setminus\{0\}$.