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AP EAMCET · Maths · Functions

The real valued function f(x)=xex-1+x2+1 defined on R\{0} is

  1. A An odd function
  2. B An even function
  3. C Both even & odd function
  4. D Neither even nor odd function
Verified Solution

Answer & Solution

Correct Answer

(B) An even function

Step-by-step Solution

Detailed explanation

Given f(x)=xex-1+x2+1 =2x+xex-x+2ex-22(ex-1) =ex(x+2)+x-22(ex-1) Then, f(-x)=e-x(-x+2)-x-22(e-x-1) =-x+2ex-x-221ex-1 =-x+2-xex-2ex21-ex =-x+2-exx+221-ex =x-2+exx+22ex-1 ⇒f(x)=f(-x) Therefore, f(x) is an even function.