How do you find the range of $f(x) = 3/x^2$ ?

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Answer 1 · 2015-07-09T20:48:39

Assuming the domain is $RR$ \ ${ 0 }$ , then the range is $(0, oo)$ .

If $x in RR$ then $x^2 >= 0$ and $3/x^2 > 0$ except when $x=0$ ..

If $x = 0$ then $x^2 = 0$ and $3/(x^2) = 3/0$ is undefined.

For any $y in (0, oo)$ if $x = sqrt(3/y)$ then $f(x) = 3/sqrt(3/y)^2 = 3/(3/y) = y$ .

So the range of $f(x)$ is the whole of $(0, oo)$

How do you find the range of f(x) = 3/x^2f(x) = 3/x^2?