Function Composition
Given the function
f
(
x
)
=
1
2
x
−
2
\displaystyle {f{{\left({x}\right)}}}=\frac{{1}}{{2}}{x}-{2}
f
(
x
)
=
2
1
x
−
2
and the function
g
(
x
)
=
8
x
2
+
2
x
+
9
\displaystyle {g{{\left({x}\right)}}}={8}{x}^{{2}}+{2}{x}+{9}
g
(
x
)
=
8
x
2
+
2
x
+
9
determine each of the following.
Give your answer as an integer or a simplified fraction.
Evaluate
f
(
g
(
5
)
)
\displaystyle {f{{\left({g{{\left({5}\right)}}}\right)}}}
f
(
g
(
5
)
)
f
(
g
(
5
)
)
=
\displaystyle {f{{\left({g{{\left({5}\right)}}}\right)}}}=
f
(
g
(
5
)
)
=
Preview
Question 6 Part 1 of 4
Evaluate
g
(
f
(
4
)
)
\displaystyle {g{{\left({f{{\left({4}\right)}}}\right)}}}
g
(
f
(
4
)
)
g
(
f
(
4
)
)
=
\displaystyle {g{{\left({f{{\left({4}\right)}}}\right)}}}=
g
(
f
(
4
)
)
=
Preview
Question 6 Part 2 of 4
Evaluate
f
(
g
(
1
6
)
)
\displaystyle {f{{\left({g{{\left(\frac{{1}}{{6}}\right)}}}\right)}}}
f
(
g
(
6
1
)
)
f
(
g
(
1
6
)
)
=
\displaystyle {f{{\left({g{{\left(\frac{{1}}{{6}}\right)}}}\right)}}}=
f
(
g
(
6
1
)
)
=
Preview
Question 6 Part 3 of 4
Evaluate
f
(
f
(
5
8
)
)
\displaystyle {f{{\left({f{{\left(\frac{{5}}{{8}}\right)}}}\right)}}}
f
(
f
(
8
5
)
)
f
(
f
(
5
8
)
)
=
\displaystyle {f{{\left({f{{\left(\frac{{5}}{{8}}\right)}}}\right)}}}=
f
(
f
(
8
5
)
)
=
Preview
Question 6 Part 4 of 4
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