Let g(x) be the inverse of an invertible function

From the definition of invertible function,

$g(f(x))=x \ldots$ (i)

So, $g(f(3))=3$, i.e., $g(9)=3$

Now, differentiating both sides of equation (i) w.r.t. $x$ using the Chain Rule of Differentiation, we get -

$g^{\prime}(f(x)), f^{\prime}(x)=1 \ldots($ ii $)$

Plugging in $x=3$ in equation (ii) gives us -

$g^{\prime}(f(3)) . f^{\prime}(3)=1$

or, $g^{\prime}(9) .9=1$

i.e., $g^{\prime}(9)=1 / 9$ (Ans)