Question

In the following case state whether the function is bijective or not. Justify your answer

f: R → R defined by f(x) = 3 – 4x²

Answer 1

f(x) = 3 – 4x²

f(1) = 3 – 4(1)² = 3 – 4 = – 1

f(2) = 3 – 4(2)² = 3 – 16 = – 13

f(3) = 3 – 4(3)² = 3 – 36 = – 33

f(4) = 3 – 4(4²) = 3 – 64 = – 61

It is not a bijective function.

The positive numbers “R” does not have a negative pre-image in X in R.