Given
f
(
x
)
=
x
3
+
7
,
g
(
x
)
=
x
−
9
and
h
(
x
)
=
x
\displaystyle {f{{\left({x}\right)}}}={x}^{{3}}+{7},\ {g{{\left({x}\right)}}}={x}-{9}\ {\quad\text{and}\quad}\ {h}{\left({x}\right)}=\sqrt{{{x}}}
f
(
x
)
=
x
3
+
7
,
g
(
x
)
=
x
−
9
and
h
(
x
)
=
x
, evaluate
h
(
f
(
g
(
x
)
)
)
\displaystyle {h}{\left({f{{\left({g{{\left({x}\right)}}}\right)}}}\right)}
h
(
f
(
g
(
x
)
)
)
h
(
f
(
g
(
x
)
)
)
=
(
x
−
9
)
3
+
7
\displaystyle {h}{\left({f{{\left({g{{\left({x}\right)}}}\right)}}}\right)}={\left(\sqrt{{{x}}}-{9}\right)}^{{3}}+{7}
h
(
f
(
g
(
x
)
)
)
=
(
x
−
9
)
3
+
7
h
(
f
(
g
(
x
)
)
)
=
(
x
−
9
)
3
+
7
\displaystyle {h}{\left({f{{\left({g{{\left({x}\right)}}}\right)}}}\right)}={\left(\sqrt{{{x}-{9}}}\right)}^{{3}}+{7}
h
(
f
(
g
(
x
)
)
)
=
(
x
−
9
)
3
+
7
h
(
f
(
g
(
x
)
)
)
=
x
3
−
2
\displaystyle {h}{\left({f{{\left({g{{\left({x}\right)}}}\right)}}}\right)}=\sqrt{{{x}^{{3}}}}-{2}
h
(
f
(
g
(
x
)
)
)
=
x
3
−
2
h
(
f
(
g
(
x
)
)
)
=
x
3
+
7
−
9
\displaystyle {h}{\left({f{{\left({g{{\left({x}\right)}}}\right)}}}\right)}=\sqrt{{{x}^{{3}}+{7}}}-{9}
h
(
f
(
g
(
x
)
)
)
=
x
3
+
7
−
9
h
(
f
(
g
(
x
)
)
)
=
(
x
−
9
)
3
+
7
\displaystyle {h}{\left({f{{\left({g{{\left({x}\right)}}}\right)}}}\right)}=\sqrt{{{\left({x}-{9}\right)}^{{3}}+{7}}}
h
(
f
(
g
(
x
)
)
)
=
(
x
−
9
)
3
+
7
h
(
f
(
g
(
x
)
)
)
=
x
3
−
2
\displaystyle {h}{\left({f{{\left({g{{\left({x}\right)}}}\right)}}}\right)}=\sqrt{{{x}^{{3}}-{2}}}
h
(
f
(
g
(
x
)
)
)
=
x
3
−
2
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