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

1 Answer
George C.
Jul 9, 2015

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

Explanation:

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)#

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