Exercise 1.3.51 (51-54)

Question

Express the function in the form $f\circ g\circ h$.\begin{enumerate}\setcounter{enumi}{50}
\item $R(x)=\sqrt{\sqrt{x}-1}$
\item $H(x)=\sqrt[3]{2+|x|}$
\item $S(t)=\sin ^2(\cos t)$
\item $W(t)=\cos (\sqrt{	an t}+1)$
\end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}
    \item [51.] $$
\begin{array}{lll}
f:[0,+\infty) ightarrow[0,+\infty), & f(x)=\sqrt{x} . \
g:  {[1,+\infty) ightarrow[0,+\infty),} & g(x)=x-1 . \
h:[1,+\infty) ightarrow[1,+\infty), & h(x)=\sqrt{x} .
\end{array}
$$
\item[52.] 
$$
\begin{array}{ll}
f:[2,+\infty) ightarrow[\sqrt{2},+\infty), & f(x)=\sqrt[3]{x} . \
g:[0,+\infty) ightarrow[2,+\infty), & g(x)=2+x . \
h:  \mathbb{R} ightarrow[0,+\infty), & h(x)=|x| .
\end{array}
$$
\item[53.]
$$
\begin{array}{ll}
f: \mathbb{R} ightarrow \mathbb{R}, & f(t)=t^2 . \
g: \mathbb{R} ightarrow \mathbb{R}, & g(t)=\sin t . \
h: \mathbb{R} ightarrow \mathbb{R}, & h(t)=\cos t .
\end{array}
$$
\item[54.] 
$$
\begin{aligned}
&f:[1,+\infty) ightarrow[\cos 1,+\infty), \quad f(t)=\cos t.\
& g: \mathbb{R} ightarrow[1,+\infty), \quad g(t)=\sqrt{t}+1 . \
& h: \mathbb{R} ightarrow \mathbb{R}, \quad h(t)=	an t .
\end{aligned}
$$

\end{enumerate}

Exercise 1.3.51 (51-54)

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Exercise 1.3.51 (51-54)

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