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The function f(x) = x3 is bijection from R to R. Is it True or False?
  • a)
    True
  • b)
    False
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The function f(x) = x3is bijection from R to R. Is it True or False?a)...
The function f(x) = x3 is one to one as no two values in domain are assigned the same value of the function and it is onto as all R of the co domain is images of elements in the domain.
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The function f(x) = x3is bijection from R to R. Is it True or False?a)...
The function f(x) = x^3 is a bijection from R to R.

To determine if the function f(x) = x^3 is a bijection from R to R, we need to check if it is both injective (one-to-one) and surjective (onto).

Injective (One-to-One):
A function is injective if every element in the domain maps to a unique element in the range. In other words, if f(a) = f(b), then a = b.

Let's suppose f(a) = f(b):
a^3 = b^3

Taking the cube root of both sides, we get:
a = b

This shows that if f(a) = f(b), then a = b. Therefore, the function f(x) = x^3 is injective.

Surjective (Onto):
A function is surjective if every element in the range is mapped to by at least one element in the domain. In other words, for every y in the range, there exists an x in the domain such that f(x) = y.

Let's consider an arbitrary y in the range. We need to find an x such that f(x) = y.

y = x^3

Taking the cube root of both sides, we get:
x = ∛y

This shows that for any y in the range, we can find an x in the domain such that f(x) = y. Therefore, the function f(x) = x^3 is surjective.

Bijection:
Since the function f(x) = x^3 is both injective and surjective, it is a bijection from R to R.

Therefore, the correct answer is option 'A' - True.
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The function f(x) = x3is bijection from R to R. Is it True or False?a)Trueb)FalseCorrect answer is option 'A'. Can you explain this answer?
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