\(f, g, h, k(x)\)

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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