Question
Let the function g:(- , ) (- 2 , 2 ) be given by g(u)=2 ^ -1 (e^u )- 2 . Then, g is
Let the function g:(- , ) (- 2 , 2 ) be given by g(u)=2 ^ -1 (e^u )- 2 . Then, g is
C. odd and is strictly increasing in (- , )
Given that g(u)=2 ^ -1 (e^u )- 2 g(-u)=2 ^ -1 (e^ -u )- 2 = 2 ^ -1 ( 1 e^u )- 2 =2 ^ -1 (e^u )- 2 =2 [ 2 - ^ -1 (e^u ) ]- 2 = -2 ^ -1 (e^u )- 2 = 2 -2 ^ -1 (e^u )=-g(u) g is an odd function. Also g^ (u)= 2 e^u 1+e^ 2 u 0, u (- , ) g is strictly increasing on (- , ).
Related: Mathematics — Functions · All PYQ Banks