for one-one function if f(x1)=f(x2) then x1 must be equal to x2 Let f(x1)=f(x2)
|x1|−1
|x1|+1
=
|x2|−1
|x2|+1
|x1||x2|+|x1|−|x2|−1=|x1||x2|−|x1|+|x2|−1 ⇒|x1|−|x2|=|x2|−|x1| 2|x1|=2|x2| |x1|=|x2| x1=x2,x1=−x2 here x1 has two values therefore function is many one function. For onto : f(x)=
|x|−1
|x|+1
for every value of f(x) there is a value of x in domain set. If f(x) is negative then x=0 for all positive value of f(x), domain contain atleast one element. Hence f(x) is onto function.