Correct option (B) surjective but not injective
The given function is defined as
Therefore, x = 1, -1, which is odd function and there is symmetry about the origin - that is, the function is non-monotonic and noninjective - in the resultant curve as shown in the following figures:
Any line parallel to x-axis cuts the graph more than one point; hence, the function is many-to-one. Now,
Now, D > 0;1 - 4y2 ≥ 0 . That is, the range is
y ∈ [-1/2,1/2] = codomain
Hence, the function is onto. Therefore, the function is surjective but not injective.