Jee Main
Limits Continuity And Differentiability
JEE Main 2022 (Online) 26th June Morning Shift
MCQ+4 / -12022
ধর \(f,g:R \to R\) অপেক্ষক দুইটি নিম্নরূপে সংজ্ঞায়িত
\(f\left( x \right) = \left\{ {\matrix{ { - \left| {x + 3} \right|\,\,\,\,,} & {x < 0} \cr {{e^x}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,} & {x \ge 0} \cr } } \right.\)
এবং \(g\left( x \right) = \left\{ {\matrix{ {{x^2} + {k_1}x\,\,\,\,,} & {x < 0} \cr {4x + {k_2}\,\,\,\,\,,} & {x \ge 0} \cr } } \right.\)
যেখানে \({{k_1}}\),\({{k_2}}\) হল বাস্তব ধ্রুবক। যদি \(x = 0\) বিন্দুতে \({gof}\) অবকলযোগ্য হয়, তাহলে \(\left( {gof} \right)\left( { - 4} \right) + \left( {gof} \right)\left( 4 \right)\) এর মান হবে :
\(f\left( x \right) = \left\{ {\matrix{ { - \left| {x + 3} \right|\,\,\,\,,} & {x < 0} \cr {{e^x}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,} & {x \ge 0} \cr } } \right.\)
এবং \(g\left( x \right) = \left\{ {\matrix{ {{x^2} + {k_1}x\,\,\,\,,} & {x < 0} \cr {4x + {k_2}\,\,\,\,\,,} & {x \ge 0} \cr } } \right.\)
যেখানে \({{k_1}}\),\({{k_2}}\) হল বাস্তব ধ্রুবক। যদি \(x = 0\) বিন্দুতে \({gof}\) অবকলযোগ্য হয়, তাহলে \(\left( {gof} \right)\left( { - 4} \right) + \left( {gof} \right)\left( 4 \right)\) এর মান হবে :