Let the function g :(- , ) (- 2 , 2 ) be given by g ( u )=2 ⁻¹ ( e ^ u )- 2 . Then g is

Step-by-step solution

aligned & g ( u )=2 ⁻¹ ( e ^ u )- 2 & ~g ( u )= ⁻¹ ( e ^ u )- ( 2 - ⁻¹ ( e ^ u ) ) & g ( u )= ⁻¹ ( e ^ u )- ⁻¹ (e^ u ) & g (- u )= ⁻¹ ( e ^ - u )- ⁻¹ ( e ^ - u ) & g (- u )= ⁻¹ ( 1 e ^ u )- ⁻¹ ( 1 e ^u ) & g (- u )= ⁻¹ ( e ^ u )- ⁻¹ ( e ^ u )=- g ( u ) aligned Now, g( u )=2 ⁻¹ ( e ^ u )- 2 g ^ ( u )= 2 e ^ u 1+ e ^ 2 u 0 for all u (- , ) g is strictly increasing function in (- , ) . Hence, g ( u ) is odd and is strictly increasing in (- , ) .