Answer
a) f is one to one function
b) g(x) = -[x]
Work Step by Step
proof :
f is strictly decreasing.
we know that , if xf(y) .
let us assume f(a) = f(b)
if a f(b) . but according to our assumption f(a) = f(b). so it is not possible.
if a>b , then f(a) < f(b) .but according to our assumption f(a) = f(b). so this is also not possible.
then a and b have to be equal : a = b
by the definition of one to one, f is one to one function.
b) consider a function g(x) = -[x] which is a decreasing function.
g(1) = -1
g(1.5) = -1
so the function g(x) has been assigned to a same value twice.
by the definition of one to one ,g(x) is not one to one function.
