JEE MAIN - Mathematics Bengali (2022 - 26th June Morning Shift - No. 6)
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 :
$$4\left( {{e^4} + 1} \right)$$
$$2\left( {2{e^4} + 1} \right)$$
$$4{e^4}$$
$$2\left( {2{e^4} - 1} \right)$$
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