Question

Show that the function f: R → R: f(x) = x² is neither one-one nor onto.

Answer 1

We know that

f (1) = 1² = 1

f (-1) = -1² = 1

Here, f is many one

Consider – 1 in the codomain R which has no elements in R with square as – 1

Hence, – 1 ∈ R which has no pre image in R

f is many one into.