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

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Answer 1 · 2018-03-10T13:08:52

Domain: $(-oo,+2)uu(+2,+oo)$
Range: $(-oo,+oo)$

$y =1/(x-2)$

$y$ is defined for all $x in RR:x!=+2$

Hence, The domain of $y$ is $(-oo,+2)uu(+2,+oo)$

Consider:

$lim_(x->2^+) y = +oo$ and $lim_(x->2^-) y = -oo$

Hence, the range of $y$ is $(-oo,+oo)$

As can be deduced from the graphic of $f(x)$ below:

graph{1/(x-2) [-16.01, 16.02, -8.01, 8]}

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