SOLUTION: does the functions have any line(s) of symmetry?what are the lines? 1)y=1/(x^2-x-6) 2)y=((e^2x)+1)/((e^x)+1)

Algebra ->  Rational-functions -> SOLUTION: does the functions have any line(s) of symmetry?what are the lines? 1)y=1/(x^2-x-6) 2)y=((e^2x)+1)/((e^x)+1)      Log On


   

Question 63383: does the functions have any line(s) of symmetry?what are the lines?
1)y=1/(x^2-x-6)
2)y=((e^2x)+1)/((e^x)+1)
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
does the functions have any line(s) of symmetry?what are the lines?
1)y=1/(x^2-x-6)
x^2-x-6=1/y =[X^2-2(X)(0.5)+0.5^2]-0.5^2-6=(X-0.5)^2-6.25
HENCE THE CURVE IS SYMMETRIC ABOUT X=0.5
SINCE FOR X=0.5+K OR X=0.5-K,WE GET SAME VALUE OF Y =1/[K^2-6.25]
2)y=((e^2x)+1)/((e^x)+1)
THERE ARE NO LINES OF SYMMETRY