Question

How do you find the domain and range of `f(x) = 1/x`?

Answer 1

Domain: `{x|x in RR:x!=0}`
Domain interval notation `(-oo,0)uu(0,oo)`

Range: `{f(x)|f(x) in RR}`
Range interval notation `(-oo,oo)`

Explanation:

The only value in the domain excluded is when the function is undefined: `1/0`, that is when `x=0`

Domain: `{x|x in RR:x!=0}` in interval notation `(-oo,0)uu(0,oo)`

Now for the range, the function `f(x)=1/x` is continuous across the domain above.

`x -> +-oo, f(x) ->0`

`x -> 4^+, f(x) -> oo`

`x -> 4^-, f(x) -> -oo`

so the range is:

Range : `{f(x)|f(x) in RR}` or in interval notation `(-oo,oo)`

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