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

Question

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

Accepted Answer

$\mathrm{gh}(x) = ln(3 + e⁻ˣ), D_{\mathrm{gh}} = (0, ∞), R_{\mathrm{gh}} = ( \ln 3, \ln 4)$

Functions - Composite Functions

Functions - Composite Functions

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