The even function is
fx=ax+a-xax-a-x
fx=ax+1ax-1
fx=xax-1ax+1
fx=log2x+x2+1
Explanation for Correct Option:
For an even function, f-x=fx.
Option C,
f-x=-xa-x-1a-x+1=-x1-ax1+ax=xax-1ax+1
So, f-x=fx.
Explanation for Incorrect Option:
Option A
f-x=a-x+axa-x-ax=a2x+11-a2x
So, f-x≠fx.
Option B,
f-x=a-x+1a-x-1=ax+11-ax
Option D,
f-x=log2-x+-x2+1=log2-x+x2+1
Hence, option C is the correct answer.