Let S be the set of all ( , ) R R such that _ x (x^2 ) ( _e x )^ ( 1 x^2 ) x^ ( _e(1+x) )^ =0. Then which of the following is (are) correct?

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Correct answer: C. (1,-1) S

aligned & _ x x^2 ( _e x )^ 1 x^2 x^ ( _e(1+x) )^ =0 \ & _ x ( _e x )^ ( _e(x+1) )^ x^ +2 =0 aligned aligned & _ x ( _e x _e(x+1) )^ ( _e x )^ - x^ +2 =0 \ & _ x ( _e x )^ - x^ +2 =0 Put _e x=t \ & _ t t^ - (e^t )^ +2 =0 aligned As we know _ x x e^x =0 +2>0 >-2

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