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If the range of the function $f(x)=-3 x-3$ is $\{3,-6,-9,-18\}$, then which of the following elements is not in the domain of $f$ ?
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Verified Answer
The correct answer is:
-1
We have, $f(x)=-3 x-3$
(i) Let $f(x)=3$, then we get
$$
3=-3 x-3 \Rightarrow 6=-3 x \Rightarrow x=-2
$$
(ii) Let $f(x)=-6$, then we get
$$
-6=-3 x-3 \Rightarrow-3=-3 x \Rightarrow x=1
$$
(iii) Let $f(x)=-9$, then we get
$$
-9=-3 x-3 \Rightarrow-6=-3 x \Rightarrow x=2
$$
(iv) Let $f(x)=-18$, then we get
$$
-18=-3 x-3 \Rightarrow-15=-3 x \Rightarrow x=5
$$
Thus, domain of $f=\{-2,1,2,5\}$
Hence, -1 cannot be in the domain of $f$.
(i) Let $f(x)=3$, then we get
$$
3=-3 x-3 \Rightarrow 6=-3 x \Rightarrow x=-2
$$
(ii) Let $f(x)=-6$, then we get
$$
-6=-3 x-3 \Rightarrow-3=-3 x \Rightarrow x=1
$$
(iii) Let $f(x)=-9$, then we get
$$
-9=-3 x-3 \Rightarrow-6=-3 x \Rightarrow x=2
$$
(iv) Let $f(x)=-18$, then we get
$$
-18=-3 x-3 \Rightarrow-15=-3 x \Rightarrow x=5
$$
Thus, domain of $f=\{-2,1,2,5\}$
Hence, -1 cannot be in the domain of $f$.
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