Let `f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1))` . If `f(x)` is continuous and differentiable at any point, then (A) `a=1/2, b=-3/2` (B) `a=-1/2, b=3/2` (C) `a=1,b=-1` (D) none of these

Explanation

To solve the problem, we need to ensure that the function \( f(x) \) is continuous and differentiable at the points where the definition of the function changes, specifically at \( x = -1 \) and \( x = 1 \).

The function is defined as:
\[
f(x) =
\begin{cases}
\frac{1}{|x|} & \text{for } |x| \geq 1 \\
ax^2 + b & \text{for } |x| < 1
...