If $h(x) = 2x + 1$, find $h(x + 2)$
...and a second question.
Given $f(x)=x^2+1, g(x)=x-2$, then what is the domain of $f(g(x))$
$\begin{align}\text{Work: } f(g(x)) & =(x-2)^2+1 \\ & =(x-2)(x-2)+1 \\ & =x^2-4x+4+1 \\ & =x^2-4x+5 \\ & ???\end{align}$
2026-03-26 09:45:54.1774518354
Composition of functions.
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$h(x + 2) = 2x+4 +1 = 2x+5$
As for the domain of the secnod, its all the Real line, since it had no undetermined points anywhere on the real line where the function cannot be determined (points where it would return the value infinity as output that is).