Question:
Let f: R→ R be a function. Note: R denotes the set of real numbers.
\(f(x) = \left\{ \begin{array}{ll} -x, & \text{if } x < -2 \\ ax^2+bx+c, & \text{if }\ x \in[-2,2]\\ x, & \text{if } x>2 \end{array} \right.\)
Which ONE of the following choices gives the values of a, b, c that make the function f continuous and differentiable ?
Let f: R→ R be a function. Note: R denotes the set of real numbers.
\(f(x) = \left\{ \begin{array}{ll} -x, & \text{if } x < -2 \\ ax^2+bx+c, & \text{if }\ x \in[-2,2]\\ x, & \text{if } x>2 \end{array} \right.\)
Which ONE of the following choices gives the values of a, b, c that make the function f continuous and differentiable ?
\(f(x) = \left\{ \begin{array}{ll} -x, & \text{if } x < -2 \\ ax^2+bx+c, & \text{if }\ x \in[-2,2]\\ x, & \text{if } x>2 \end{array} \right.\)
Which ONE of the following choices gives the values of a, b, c that make the function f continuous and differentiable ?
Updated On: Jan 30, 2026
- \(a=\frac{1}{4},b=0,c=1\)
- \(a=\frac{1}{2},b=0,c=0\)
- a = 0, b = 0, c = 0
- a = 1, b = 1, c = -4
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The Correct Option is A
Solution and Explanation
The correct option is (A) : \(a=\frac{1}{4},b=0,c=1\).
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