Let f : [0, +?) ? (0, 1] be the function from the set [0, +?) to the set
(0, 1] defined such that
f (x) =1/(1 + x^2)
for all x ? [0, +?), where
[0, +?) = {x ? R : 0 ? x < +?}, (0, 1] = {x ? R : 0 < x ? 1}.
(Thus [0, +?) is the set consisting of all non-negative real numbers.)
Determine whether or not the function f is injective, whether or not it
is surjective, and whether or not it is invertible.
I absolutely cannot do this one. Can anybody put me on track?
(0, 1] defined such that
f (x) =1/(1 + x^2)
for all x ? [0, +?), where
[0, +?) = {x ? R : 0 ? x < +?}, (0, 1] = {x ? R : 0 < x ? 1}.
(Thus [0, +?) is the set consisting of all non-negative real numbers.)
Determine whether or not the function f is injective, whether or not it
is surjective, and whether or not it is invertible.
I absolutely cannot do this one. Can anybody put me on track?