## Question 10: Let the function y=f(x) be continuous on (mathbb{R}) and have a graph of the function (y=f'(x)) as shown below. On what interval is the function (g(x)=f(1-x)+frac{x^{2}}{2}-x) inverse?

Question 10: Let the function y=f(x) be continuous on (mathbb{R}) and have a graph of the function (y=f'(x)) as shown below. On what interval is the function (g(x)=f(1-x)+frac{x^{2}}{2}-x) inverse? A. (((1 ; 3)) B. ((-thirty first)) C. (left(-1 ; frac{3}{2}right)) D. ((-2 ; 0)) (begin{array}{l} g^{prime}(x)=-f^{prime}(1-x)+x-1, forall mathrm{x} in mathbb{R } \ g^{prime}(x)=-f^{prime}(1-x)+x-1 leq 0 …