Check whole-domain composition before finding its range

The functions $f$ and $g$ are defined by

$f:x\mapsto\sin\left(x+\dfrac\pi4\right)$, $x\in\mathbb R$, $-\dfrac\pi2\leq x\leq\dfrac\pi2$,

$g:x\mapsto\ln(2-x)$, $x\in\mathbb R$, $x<2$.

Explain whether the following composite function exist

(a) $gf$

(b) $fg$

If the composite function exists, determine the rule, domain and range.5 marks