APFIVE Derivative of an Inverse Function
The function $$f$$ is invertible and is defined by $$f(x)=\sqrt{1+x^2}$$. If $$g$$ is the inverse of $$f$$, what is the value of $$g'(\sqrt{2})$$?
The table below shows selected values for $$f$$.
| x | f(x) |
|---|---|
| 0 | 1 |
| 1 | $$\sqrt{2}$$ |
| 2 | $$\sqrt{5}$$ |
A
$$\sqrt{2}$$
B
$$2$$
C
$$\frac{1}{\sqrt{2}}$$
D
$$1+\sqrt{2}$$
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