Question

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

f: R → R defined by f(x) = 2x + 1

Answer 1

f(x) = 2x + 1

f(0) = 2(0) + 1 = 0 + 1 = 1

f(1) = 2(1) + 1 = 2 + 1 = 3

f(2) = 2(2) + 1 = 4 + 1 = 5

f(3) = 2(3) + 1 = 6 + 1 = 7

Different elements has different images

∴ It is an one-one function.

It is also an onto function.

The function is one-one and onto function.

∴ It is a bijective function.