Welcome to Bytelearn!

Let’s check out your problem:

(a)$\newline$$$\begin{array}{l} f(x)=\frac{1}{6 x}, x \neq 0 . \\ g(x)=\frac{1}{6 x}, x \neq 0 . \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$$$\newline$$f$ and $g$ are inverses of each other$\newline$$f$ and $g$ are not inverses of each other$\newline$(b) $f(x)=x+2$$\newline$$$\begin{array}{l} g(x)=x+2 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$$$\newline$$f_{\text {and }} \boldsymbol{g}$ are inverses of each other$\newline$$f$ and $g$ are not inverses of each other