# $$f, g, h, k(x)$$

Algebra Level 3

The function $$f(x) = \frac{1}{1+x}$$ is defined for all real values $$x\neq -1,$$ and the functions $$f, g, \mbox{ and } h$$ satisfy the equations $f(g(x)) = x+1 \mbox{ and } h(f(x)) = x + 2.$ If $$k(x) = g(x) + h(x),$$ then what is $$k(4)?$$

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