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If a function f: R R is defined as f(x)=x^2+1 , then the pre-image of -3 is

Options

  1. A-4,4
  2. B- 2 , 2
  3. C-2,2

Correct answer

3

Step-by-step solution

The pre-image of a value y under a function f(x) is the set of all x such that f(x) = y . Given f(x) = x^2 + 1 , we set f(x) = -3 . x^2 + 1 = -3 x^2 = -3 - 1 x^2 = -4 Since the square of any real number x must be non-negative ( x^2 0 for all x R ), there is no real number x such that x^2 = -4 . Therefore, the set of pre-images is the empty set, denoted by . Answer:

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