Consider the function. f(x)=\ cc (a(7 x-12-x²))/(b|x²-7 x+12|), x 3 ~b, x=3,. where [x] denotes the greatest integer less than or equal to x. If S denotes the set of all ordered pairs (a, b) such that f(x) is continuous at x=3, then the number of elements in S is:

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 27 Jan, Morning shift · Q4161

JEE Main 202427 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Consider the function.

f(x)=\left\{\begin{array}{cc} \frac{\mathrm{a}\left(7 x-12-x^2\right)}{\mathrm{b}\left|x^2-7 x+12\right|} & , x<3 \\\\ 2^{\frac{\sin (x-3)}{x-[x]}} & , x>3 \\\\ \mathrm{~b} & , x=3, \end{array}\right.

where

[x]

denotes the greatest integer less than or equal to

x

. If

\mathrm{S}

denotes the set of all ordered pairs (a, b) such that

f(x)

is continuous at

x=3

, then the number of elements in

\mathrm{S}

is :