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

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Answer 1 · 2015-08-11T10:28:06

Domain: $(- \infty, 1) \cup (1, + \infty)$ $(-oo, 1) uu (1, +oo)$
Range: $(- \infty, 0) \cup (0, + \infty)$ $(-oo, 0) uu (0, + oo)$

The domain of the function will be restricted by the fact that the denominator cannot be equal to zero.

$x - 1 \neq 0 \Rightarrow x \neq 1$ $x-1!=0 implies x!=1$

The domain will thus be $RR-{1}$ , or $(-oo, 1) uu (1, +oo)$ .

The range of the function will be restricted by the fact that this expression cannot be equal to zero, since the numerator is a constant.

The range of the function will thus be $RR-{0}$ , or $(-oo, 0) uu (0, + oo)$ .

graph{2/(x-1) [-7.9, 7.9, -3.95, 3.95]}

What is the domain and range of g(x)= 2/ (x-1)g(x)=2x−1g(x)= 2/ (x-1)?