AIEEE math sample practice questions in Functions about finding the range of a function. Fermat Education - AIEEE Classes

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Functions : Range of a function

Question 2
The range of the function (x^2 + 4x + 7)/(x^2 + 4x + 6) is
  1. [1, 3/2)
  2. (1, 3/2]
  3. [1, 3/2]
  4. [0, 3]
Correct Answer is (1, 3/2]. Choice (2)

Explanatory Answer

The expression can also be written as 1 + 1/(x^2 + 4x + 6) or 1 + 1/(x+2)^2+2).

The lower bound of this expression is 1, while the upper bound is reached when x = -2.

The expression will always be greater than 1, so the lower bound is non-inclusive.

The upper bound of 3/2 can be reached when x = -2.

The correct range is (1, 3/2], or choice (2).



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