Let `f:RtoR:f(x)=xandg:RtoR:g(x)=|x|` be the identity function and the modulus function respectively.
Now, dom `((f)/(g))="dom "(f)nn"dom "(g)-{x:g(x)=0}`
and `{x:g(x)=0}={x:""|x|=0}={0}`.
`:."dom "((f)/(g))=[RnnR-{0}]-{0}=R-{0}`
So, `(f)/(g):R-{0}toR:((f)/(g))(x)=(f(x))/(g(x))=(x)/(|x|)={{:(1",when "xgt0),(-1",when "xlt0):}`
Hence, `((f)/(g))(x)={{:(1",when "xgt0),(-1",when "xlt0):}`.