Let f(x)=(1+b^2)x^2+2bx+1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

JEE Main Mathematics question

Let and let be the minimum value of . As varies, the range of is

Answer: (D)

The coefficient , so the parabola opens upwards and the minimum is at . Minimum value: (using

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Question ID VK-007715