Write whether f : R → R given by is one-one, many-one, onto or into.

(I)A function is one-one function or an injection if

f(x)=f(y)x=y for all x,yA

or f(x)f(y)xy for all x,yA

(II) A function is onto function or surjection if

Range (f)=co-domain(f)

(III) A function is not onto function, then

is always an onto function

Given:-

(i)f : R → R

(ii)

=x ± x

=0, 2x

Now putting x=0

Again putting x=-1

Hence f is many one