AP EAMCET201920 Apr 2019Morning ShiftMathematicsFunctionsActual
(f(x)= x e^x-1 + x 2 +2 ^3 x 2 ) on (R- 0 ) is
Options
- Aone one function
- Bbijection
- Calgebraic function
- Deven function
Correct answer
D. even function
Step-by-step solution
Given function (f(x)= x e^x-1 + x 2 +2 ^3 x 2 ) on (R- 0 ). ( aligned f(-x) & = -x e^ -x -1 - x 2 +2 ^3 (- x 2 ) & = -x e^x 1-e^x - x 2 +2 ^3 x 2 & = x e^x e^x-1 - x 2 +2 ^3 x 2 & = x (e^x-1+1 ) e^x-1 - x 2 +2 ^3 x 2 & =x+ x e^x-1 - x 2 +2 ^3 x 2 & = x e^x-1 + x 2 +2 ^3 x 2 =f(x) aligned ) ( f(-x)=f(x), x R- 0 ) ( f(x) ) is an even function. Hence, option (4) is correct.