In the following case state whether the function is bijective or … - Vidyadip

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

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Answer

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.

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