Which of the following is a bijective function?

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Beltron Programmer 1 Oct 2023 Official Paper

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Answer 1

The correct answer is y = x + 10.

Key Points

A function is bijective if it is both injective (one-to-one) and surjective (onto).
Injective: A function is injective if every element of the domain maps to a unique element in the codomain.
Surjective: A function is surjective if every element in the codomain has a preimage in the domain.
For y = x + 10, the function is linear and satisfies both injective and surjective properties:
- Injective: Since the slope of the line is non-zero, each x value maps to a unique y value.
- Surjective: Any real number y can be achieved by solving for x (x = y - 10), ensuring that all values in the codomain have a preimage.

Additional Information

y = cos x: Not bijective because it is periodic and does not cover all real numbers (not surjective).
y = x²: Not bijective because multiple x values (positive and negative) map to the same y value (not injective).
y = |x|: Not bijective because multiple x values (positive and negative) map to the same y value (not injective).
Bijective functions are particularly important in mathematics as they define one-to-one correspondences between sets.