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Let f(x) = { (ax^2 + 2ax + 3)/(4x^2 + 4x - 3) ; x ≠ -3/2, 1/2 b ; x = -3/2, 1/2 } be continuous at x = -3/2. If f(0) = 7/5, then x is equal to :

1. 2
2. 1
3. 0
4. 1.4

Correct answer: 2

Solution

The function must be continuous at x = -3/2, meaning the limit as x approaches -3/2 from both sides must equal the value of the function at that point. Given that f(0) = 7/5, we can substitute x = 0 into the function and solve for 'a', leading to the conclusion that 'a' must equal 2 for the function to satisfy the continuity condition.

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