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Which of the following function is injective?

Options

  1. Af(x)= 4 x^2+3 x-5 4+3 x-5 x^2 , x (- , )
  2. Bf(x)=(x-4)(x-5), x (- , )
  3. Cf(x)=|x+2|, x [-2, )
  4. Df(x)=x^2+2, x (- , )

Correct answer

C. f(x)=|x+2|, x [-2, )

Step-by-step solution

A function f(x) is injective if f(x₁) = f(x₂) implies x₁ = x₂ . For option (LZ8Jm), the function f(x) = 4x^2 + 3x - 5 4 + 3x - 5x^2 is a rational function. It is not injective as it is not monotonic over its entire domain. For option (fCqBV), f(x) = (x-4)(x-5) = x^2 - 9x + 20 . This is a parabola opening upwards, which is not injective on (- , ) because f(4) = f(5) = 0 . For option (bVs0N), f(x) = |x+2| for x [-2, ) . Since x -2 , x+2 0 , so f(x) = x+2 . This is a linear function with a positive slope, which is str

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