Consider the composite function
w
(
x
)
=
f
(
g
(
h
(
x
)
)
)
=
\displaystyle {w}{\left({x}\right)}={f{{\left({g{{\left({h}{\left({x}\right)}\right)}}}\right)}}}=
w
(
x
)
=
f
(
g
(
h
(
x
)
)
)
=
x
5
−
9
\displaystyle \sqrt{{{x}^{{5}}-{9}}}
x
5
−
9
Which of the following is a possible solution for
f
(
x
)
\displaystyle {f{{\left({x}\right)}}}
f
(
x
)
,
g
(
x
)
\displaystyle {g{{\left({x}\right)}}}
g
(
x
)
and
h
(
x
)
\displaystyle {h}{\left({x}\right)}
h
(
x
)
.
f
(
x
)
=
x
−
9
\displaystyle {f{{\left({x}\right)}}}={x}-{9}
f
(
x
)
=
x
−
9
,
g
(
x
)
=
x
5
\displaystyle {g{{\left({x}\right)}}}={x}^{{5}}
g
(
x
)
=
x
5
and
h
(
x
)
=
x
\displaystyle {h}{\left({x}\right)}=\sqrt{{{x}}}
h
(
x
)
=
x
f
(
x
)
=
x
5
\displaystyle {f{{\left({x}\right)}}}={x}^{{5}}
f
(
x
)
=
x
5
,
g
(
x
)
=
x
−
9
\displaystyle {g{{\left({x}\right)}}}={x}-{9}
g
(
x
)
=
x
−
9
and
h
(
x
)
=
x
\displaystyle {h}{\left({x}\right)}=\sqrt{{{x}}}
h
(
x
)
=
x
f
(
x
)
=
x
−
9
\displaystyle {f{{\left({x}\right)}}}={x}-{9}
f
(
x
)
=
x
−
9
,
g
(
x
)
=
x
5
\displaystyle {g{{\left({x}\right)}}}={x}^{{5}}
g
(
x
)
=
x
5
and
h
(
x
)
=
x
\displaystyle {h}{\left({x}\right)}=\sqrt{{{x}}}
h
(
x
)
=
x
f
(
x
)
=
x
+
2
\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}+{2}}}
f
(
x
)
=
x
+
2
,
g
(
x
)
=
x
−
11
\displaystyle {g{{\left({x}\right)}}}={x}-{11}
g
(
x
)
=
x
−
11
and
h
(
x
)
=
x
5
\displaystyle {h}{\left({x}\right)}={x}^{{5}}
h
(
x
)
=
x
5
f
(
x
)
=
x
\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}}}
f
(
x
)
=
x
,
g
(
x
)
=
x
5
\displaystyle {g{{\left({x}\right)}}}={x}^{{5}}
g
(
x
)
=
x
5
and
h
(
x
)
=
x
−
9
\displaystyle {h}{\left({x}\right)}={x}-{9}
h
(
x
)
=
x
−
9
f
(
x
)
=
x
5
\displaystyle {f{{\left({x}\right)}}}=\sqrt{{{x}^{{5}}}}
f
(
x
)
=
x
5
,
g
(
x
)
=
x
−
11
\displaystyle {g{{\left({x}\right)}}}={x}-{11}
g
(
x
)
=
x
−
11
and
h
(
x
)
=
x
+
2
\displaystyle {h}{\left({x}\right)}={x}+{2}
h
(
x
)
=
x
+
2
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