If f ^ (x)= ⁻¹( x+ x),- 2 < x < 2 and f(0)=0 , then f(1) is

Step-by-step solution

aligned f^ (x) & = ⁻¹( x+ x) & = ⁻¹ ( 1+ x x ) & = ⁻¹ [ ( x 2 + x 2 )^2 ^2 x 2 - ^2 x 2 ] & = ⁻¹ ( x 2 + x 2 x 2 - x 2 ) & = ⁻¹ [ 1+ x 2 1- x 2 ) & = ⁻¹ [ ( 4 + x 2 ) ] aligned aligned f ^ (x) & = 4 + x 2 f (x) & = ( 4 + x 2 ) d x & = x 4 + 1 2 x^2 2 + c aligned array ll f(0)=c & c=0 & [ f(0)=0 (given) ] array array r f (x)= x 4 + x^2 4 f (1)= +1 4 array