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The domain of the function y= 1 ₁₀(3-x) + x+7 is

Options

  1. A(-7,3)
  2. B(-7,3)- 0
  3. C[-7,3)- 2
  4. D[-7,3]- 1

Correct answer

C. [-7,3)- 2

Step-by-step solution

The function is defined if the following conditions are satisfied: 1. The argument of the square root must be non-negative: x + 7 0 x -7 . 2. The argument of the logarithm must be positive: 3 - x > 0 x 3. The denominator must not be zero: ₁₀(3 - x) 0 . Solving ₁₀(3 - x) = 0 gives 3 - x = 10^0 = 1 , which implies x = 2 . Combining these conditions, we have x [-7, 3) and x 2 . Therefore, the domain is [-7, 3) - 2 . Answer: [-7,3)- 2

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