Question

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

Answer 1

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

Explanation:

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]}