Let $f(x)=\left\{\begin{array}{ccc}a x-b, & x \leq 1 \\ 3 x, & 1 < x < 2 \\ b x^2-a, & x \geq 2\end{array}\right.$ If $f$ is continuous function then $(a, b)$ is equal to

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Application +4 | -1

Let

f(x)=\left\{\begin{array}{ccc}a x-b, & x \leq 1 \\ 3 x, & 1 < x < 2 \\ b x^2-a, & x \geq 2\end{array}\right.

f

is continuous function then

(a, b)

is equal to

View answer and explanation

Correct option: D

(6,3)

Option D ((6,3)) is correct because for f to be continuous, the left and right limits at x=1 and x=2 must be equal, leading to the solution a=6 and b=3.

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