Question

Which of the following options is/are true for the function $f\left(x\right)=-\frac{1}{x}$

Answer 1

$f\left(x\right)=-\frac{1}{x}$
Clearly, domain is $R-\left\{0\right\}$ and range is $R-\left\{0\right\}.$

We know that, graph of $\frac{1}{x}$ is


$\therefore$ graph of $-\frac{1}{x}$ will be


Here, from we can see that $f\left(x\right)$ takes all the values except $0$, therefore the range of $f\left(x\right)$ is $R-\left\{0\right\}.$