# A calculus problem by Brilliant Member

Calculus Level 3

$f(x)=-4\sqrt { { e }^{ 1-{ x } } } +1+{ x }+\frac { { x }^{ 2 } }{ 2 } +\frac { { x }^{ 3 } }{ 3 }$

If $$g(x)$$ is the inverse of $$f(x)$$ above, then find $$\dfrac 2 {g' \left(\frac {-7}6\right)}$$, where $$g'$$ is the first derivative of $$g$$.

×