$g: x \mapsto \ln(1 + x),\ x \in \mathbb{R},\ x -1$ and $h: x \mapsto 2 + e^{-x},\ x \in \mathbb{R

Question

$g: x \mapsto \ln(1 + x),\ x \in \mathbb{R},\ x > -1$ and $h: x \mapsto 2 + e^{-x},\ x \in \mathbb{R}^+$. Determine, with reasons, whether $gh$ and $hg$ exist. If the composite function exists, give the rule, domain and range in exact form.

Accepted Answer

$gh(x) = ln(3 + e^{-x}); D_{gh} = (0, ∞); R_{gh} = (ln 3, ln 4)$

Worked Example 2

Worked Example 2

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