If the range of the function f(x) = -3x - 3 i | vedclass

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Question

(A) Given the function $f(x) = -3x - 3$. To find the domain, we set $f(x)$ equal to each element in the range: $(i)$ For $f(x) = 3$: $3 = -3x - 3$ $\R

Vedclass · Accepted Answer

-$1$

Vedclass · Answer

(A) Given the function $f(x) = -3x - 3$. To find the domain, we set $f(x)$ equal to each element in the range: $(i)$ For $f(x) = 3$: $3 = -3x - 3$ $\Rightarrow 6 = -3x$ $\Rightarrow x = -2$. (ii) For $f(x) = -6$: $-6 = -3x - 3$ $\Rightarrow -3 = -3x$ $\Rightarrow x = 1$. (iii) For $f(x) = -9$: $-9 = -3x - 3$ $\Rightarrow -6 = -3x$ $\Rightarrow x = 2$. (iv) For $f(x) = -18$: $-18 = -3x - 3$ $\Rightarrow -15 = -3x$ $\Rightarrow x = 5$. Thus, the domain of $f$ is $\{-2, 1, 2, 5\}$. Comparing this with the given options, $-1$ is not in the domain of $f$.

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

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