Function Composition Using Rule of 4
Use the functions for
f
(
x
)
\displaystyle {f{{\left({x}\right)}}}
f
(
x
)
,
g
(
x
)
\displaystyle {g{{\left({x}\right)}}}
g
(
x
)
,
h
(
x
)
\displaystyle {h}{\left({x}\right)}
h
(
x
)
and
p
(
t
)
\displaystyle {p}{\left({t}\right)}
p
(
t
)
to evaluate the expressions below. Write your answer as an integer or a reduced fraction.
f
(
−
1
+
g
(
−
1
)
)
=
\displaystyle {f{{\left(-{1}+{g{{\left(-{1}\right)}}}\right)}}}=
f
(
−
1
+
g
(
−
1
)
)
=
g
(
h
(
−
2
)
−
3
)
=
\displaystyle {g{{\left({h}{\left(-{2}\right)}-{3}\right)}}}=
g
(
h
(
−
2
)
−
3
)
=
p
(
f
(
2
)
+
h
(
2
)
)
=
\displaystyle {p}{\left({f{{\left({2}\right)}}}+{h}{\left({2}\right)}\right)}=
p
(
f
(
2
)
+
h
(
2
)
)
=
f
(
g
(
h
(
−
4
)
)
=
\displaystyle {f{{\left({g{{\left({h}{\left(-{4}\right)}\right)}}}=\right.}}}
f
(
g
(
h
(
−
4
)
)
=
h
(
x
)
=
−
x
+
1
\displaystyle {h}{\left({x}\right)}=-{x}+{1}
h
(
x
)
=
−
x
+
1
g
(
x
)
\displaystyle {g{{\left({x}\right)}}}
g
(
x
)
: {(-4,-4), (-3,-1), (-2,4), (-1,1), (0,2), (1,3), (2,5), (3,-2), (4,-3), (5,0)}
t
\displaystyle {t}
t
-4
-3
-2
-1
0
1
2
3
4
5
p
(
t
)
\displaystyle {p}{\left({t}\right)}
p
(
t
)
3
-2
2
-3
0
5
4
-1
-4
1
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