Question

What is the domain and range of `F(x) = 5/(x-2)`?

Answer 1

`text(Domain): x!=2`
`text(Range): f(x)!=0`

Explanation:

The domain is the range of `x` values which give `f(x)` a value that is unique, such there is only one `y` value per `x` value.

Here, since the `x` is on the bottom of the fraction, it cannot have any value such that the whole denominator equals zero, i.e. `d(x)!=0` `d(x)=text(denominator of the fraction that is a function of)` `x`.

`x-2!=0`
`x!=2`

Now, the range is the set of `y` values given for when `f(x)` is defined. To find any `y` values that cannot be reached, i.e. holes, asymptotes, etc. We rearrange to make `x` the subject.

`y=5/(x-2)`

`x=5/y+2`, `y!=0` since this would be undefined, and so there are no values of `x` where `f(x)=0`. Therefore the range is `f(x)!=0`.