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The graph is represented by which of the following function?
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Verified Answer
The correct answer is:
$f(x)=\sqrt{|x-1|-1}$
The domain of $f(x)=\sqrt{|x-1|-1}$ is $(-\infty, 0] \cup$ $[2, \infty)$ because $|x-1| \geq 1$. Now
$x \leq 0 \Rightarrow f(x)=\sqrt{|x-1|-1}=\sqrt{-x}$
So the graph must be upper half the parabola $y^2=-x$ with vertex at origin. Again
$x \geq 2 \Rightarrow y=\sqrt{x-2} \Rightarrow y^2=x-2$
which represents parabola in the upper half of the $x$-axis with vertex at $(2,0)$.
$x \leq 0 \Rightarrow f(x)=\sqrt{|x-1|-1}=\sqrt{-x}$
So the graph must be upper half the parabola $y^2=-x$ with vertex at origin. Again
$x \geq 2 \Rightarrow y=\sqrt{x-2} \Rightarrow y^2=x-2$
which represents parabola in the upper half of the $x$-axis with vertex at $(2,0)$.
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