the function f(x)=(x/(ex-1))+(x/2)+1 is
(a) even (b)periodic (c) odd (d) neither even nor odd
plz give the solution to this
To find whether the function is even or odd:
f(-x)=((-x)/(e-x-1)+(-x/2)+1
= -(( x/1-ex)/ex) -x/2 + 1
=xex/(ex-1) - x/2+1
f(-x) is neither equal to f(x) nor minus f(x)
Therefore f(x) is not odd and also not even
From the given terms it is known that f(x) is not periodic
because x,e^x are not periodic
Therefore the final answer is (d)neither even nor odd
Which option is correct ?
f(-x)=xex/(ex-1)-x/2+1
=x[(ex-1)+1]/(ex-1)-x/2+1
=x[1+1/(ex-1)]-x/2+1
=x+x/(ex-1)-x/2+1
=x/(ex-1)+x/2+1=f(x)
Therefore it is an even function.