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

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Answer 1 · 2015-08-16T16:37:50

Domain: $(-oo, 2) uu (2, + oo)$
Range: $(-oo, 0) uu (0, + oo)$

Your function is defined for any value of $in RR$ except the one that can make the denominator equal to zero.

$x-2 = 0 implies x = 2$

This means that $x = 2$ will be excluded from the domain of the function, which will thus be $RR - {2}$ , or $(-oo, 2) uu (2, + oo)$ .

The range of the function will be affected by the fact that the only way a fraction can be equal to zero is if the numerator is equal to zero.

In your case, the numerator is constant, euqal to $1$ regardless of the value of $x$ , which implies that the function can never be equal to zero

$f(x) != 0", "(AA)x in RR-{2}$

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

graph{1/(x-2) [-10, 10, -5, 5]}

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