If f(x)= ⁻¹ ( 3 x-x^3 1-3 x^2 ) and g(x)= ⁻¹ ( 1-x^2 1+x^2 ) , then _ x a f(x)-f(a) g(x)-g(a) , 0 a 1 2 , i

Step-by-step solution

Given that, f(x)= ⁻¹ ( 3 x-x^3 1-3 x^2 ) and g(x)= ⁻¹ ( 1-x^2 1+x^2 ) Put x= in f(x) , we get aligned f(x) & = ⁻¹ ( 3 - ^3 1-3 ^2 ) f(x) & = 2 -3 ⁻¹ x aligned Again put x= in g(x) , we get aligned & g(x)= ⁻¹ ( 1- ^2 1+ ^2 ) & g(x)=2 ⁻¹ x & _ x a f(x)-f(a) g(x)-g(a) & = _ x a ( 2 -3 ⁻¹ x )- 2 +3 ⁻¹ a 2 ⁻¹ x-2 ⁻¹ a & = _ x a -3 ( ⁻¹ a- ⁻¹ x ) 2 ( ⁻¹ a- ⁻¹ x ) =- 3 2 aligned