Let, y=1+x2x
⇒y+yx2−x=0
⇒x2y−x+y=0
⇒x=2y+1±1−4y2
⇒1−4y2≥0
⇒4y2≤1
⇒ So, y∈[−21,21]
Here, Co-Domain=Range
Hence, the function is surjective.
Now, for injective function
⇒1+x12x1=1+x22x2
⇒x1+x2x22−x2−x2x12=0
⇒(x1−x2)+x1x2(x2−x1)=0
⇒(x2−x1)(x1x2−1)=0
⇒x2=x1 or x1=x21
Hence, the function is not injective.