It is given that
f(x) = 1 + x2
By substituting values we get
f(-1) = 1 + (-1)2 = 2
f(1) = 1 + 12 = 2
Hence, f is many one.
Consider y = 1 + x2
It can be written as
x = √(y – 1)
If y <1 then we know that √(y – 1) is imaginary
O ∈ R has no pre image in R
Hence, f is into.