APFIVE Solving a Composite Function Equation
For the function
$$f(x)=\frac{1}{x+4},$$
find all values of x such that
$$f(f(x)) = x.$$
| Function | Expression |
|---|---|
| $$f(x)$$ | $$\frac{1}{x+4}$$ |
A
$$x = \frac{1}{x+4}$$
B
$$x = -2-\sqrt{5}$$
C
$$x = -2+\sqrt{5} \text{ and } x = -2-\sqrt{5}$$
D
$$x = -2+\sqrt{5}$$
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