Question

If the range of the function $f\left(x\right)=-3x-3$ is $\{3,-6,-9,-18\}$, then which of the following elements is not in the domain of $f$?

• A. $0$
• B. $-2$
• C. $1$
• D. $2$

Answer 1

The correct option is A $0$

Given, $f\left(x\right)=-3x-3$
Range of $f=\{3,-6,-9,-18\}$
Now, check all the numbers from the options and see if their $f\left(x\right)$ lies in the range:

For $x-0$, $f\left(0\right)=-3\times 0-3=-3$

Thus $0$ cannot belong to the domain of $f\left(x\right)$

While for the other numbers:

For $x-0$, $f(-2)=(-3\times -2)-3=3$

For $x-0$, $f\left(1\right)=(-3\times 1)-3=-6$

For $x-0$, $f\left(2\right)=(-3\times 2)-3=-9$

All of the above values lie in the range while, $-3$ does not lie.

Thus $0$ cannot be in the domain of $f\left(x\right)$