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

Step-by-step solution

aligned & f ^ ( x )= ⁻¹( x + x )= ⁻¹ ( 1+ x x ) & = ⁻¹ ( x 2 + x 2 x 2 - x 2 )= ⁻¹ ( ( 4 + x 2 ) ) & = 4 + x 2 aligned Now f(x)= f^ (x) d x= ( 4 + x 2 ) d x= 4 x+ x^2 4 +C f (0)=0 c =0 Hence, f(x)= x^2+ x 4 f (1)= 1^2+ 1 4 = +1 4