APFIVE Derivative of an Inverse Function from a Table
Selected values of the increasing function $$h$$ and its derivative $$h'$$ are shown in the table above. If $$g$$ is a differentiable function such that $$h(g(x)) = x$$ for all $$x$$, what is the value of $$g'(7)$$?
| $$x$$ | $$3$$ | $$7$$ |
|---|---|---|
| $$h(x)$$ | $$7$$ | $$22$$ |
| $$h'(x)$$ | $$5$$ | $$10$$ |
A
$$-\frac{1}{10}$$
B
$$\frac{1}{10}$$
C
$$\frac{7}{5}$$
D
$$\frac{1}{5}$$
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