Let f be real-valued function such that e^ -2 x f(x)=x+3+ ₀^x d t t^6+1 for all x (-1,1) and let y=g(x) be a function whose graph is reflection of the graph of y=f(x) w.r.t. line y=x , then g^ (3) is not equal to:

Step-by-step solution

Clearly g(x)=f⁻¹(x) aligned & g^ (f(x))= 1 f^ (x) & g^ (3)= 1 f^ (0) aligned array ll & f(x)=e^ 2 x +2(x+3) e^ 2 x +2 e^ 2 x ₀^x d t t^6+1 +e^ 2 x ( 1 x^6+1 ) & f^ (0)=1+6+0+1=8 & g^ (3)= 1 8 array