What is the domain and range of $y = \frac{1}{{(x - 1)}^{2}}$ $y=1/(x-1)^2$ ?

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What is the domain and range of $y = \frac{1}{{(x - 1)}^{2}}$ $y=1/(x-1)^2$ ?

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Answer 1 · 2018-01-15T11:05:52

Domain: $x in RR$ , $x ne 1$ .
Range: $y>0$

Explanation:

The graph of $y=1/x^2$ has domain $x in RR$ , $x ne 0$ and $y>0$ .

$y=1/(x-1)^2$ is a horizontal shift of 1 unit to the right, so the new domain is $x in RR$ , $x ne 1$ . The range does not change, so it's still $y>0$ .

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What is the domain and range of $y = \frac{1}{{(x - 1)}^{2}}$ $y=1/(x-1)^2$ ?

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What is the domain and range of $y = \frac{1}{{(x - 1)}^{2}}$ $y=1/(x-1)^2$ ?