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Let’s check out your problem:
Given the definitions of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
below, find the value of
f
(
g
(
2
)
)
f(g(2))
f
(
g
(
2
))
.
\newline
f
(
x
)
=
−
3
x
−
1
g
(
x
)
=
3
x
2
−
6
x
+
8
\begin{array}{l} f(x)=-3 x-1 \\ g(x)=3 x^{2}-6 x+8 \end{array}
f
(
x
)
=
−
3
x
−
1
g
(
x
)
=
3
x
2
−
6
x
+
8
\newline
Answer:
View step-by-step help
Home
Math Problems
Algebra 1
Write variable expressions for arithmetic sequences
Full solution
Q.
Given the definitions of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
below, find the value of
f
(
g
(
2
)
)
f(g(2))
f
(
g
(
2
))
.
\newline
f
(
x
)
=
−
3
x
−
1
g
(
x
)
=
3
x
2
−
6
x
+
8
\begin{array}{l} f(x)=-3 x-1 \\ g(x)=3 x^{2}-6 x+8 \end{array}
f
(
x
)
=
−
3
x
−
1
g
(
x
)
=
3
x
2
−
6
x
+
8
\newline
Answer:
Find
g
(
2
)
g(2)
g
(
2
)
:
First, we need to find the value of
g
(
2
)
g(2)
g
(
2
)
using the definition of
g
(
x
)
g(x)
g
(
x
)
.
\newline
g
(
x
)
=
3
x
2
−
6
x
+
8
g(x) = 3x^2 - 6x + 8
g
(
x
)
=
3
x
2
−
6
x
+
8
\newline
So,
g
(
2
)
=
3
(
2
)
2
−
6
(
2
)
+
8
g(2) = 3(2)^2 - 6(2) + 8
g
(
2
)
=
3
(
2
)
2
−
6
(
2
)
+
8
Calculate
g
(
2
)
g(2)
g
(
2
)
:
Now, let's calculate
g
(
2
)
g(2)
g
(
2
)
.
g
(
2
)
=
3
(
4
)
−
12
+
8
g(2) = 3(4) - 12 + 8
g
(
2
)
=
3
(
4
)
−
12
+
8
g
(
2
)
=
12
−
12
+
8
g(2) = 12 - 12 + 8
g
(
2
)
=
12
−
12
+
8
g
(
2
)
=
8
g(2) = 8
g
(
2
)
=
8
Use
g
(
2
)
g(2)
g
(
2
)
for
f
(
g
(
2
)
)
f(g(2))
f
(
g
(
2
))
:
Next, we use the value of
g
(
2
)
g(2)
g
(
2
)
to find
f
(
g
(
2
)
)
f(g(2))
f
(
g
(
2
))
using the definition of
f
(
x
)
f(x)
f
(
x
)
.
f
(
x
)
=
−
3
x
−
1
f(x) = -3x - 1
f
(
x
)
=
−
3
x
−
1
So,
f
(
g
(
2
)
)
=
f
(
8
)
=
−
3
(
8
)
−
1
f(g(2)) = f(8) = -3(8) - 1
f
(
g
(
2
))
=
f
(
8
)
=
−
3
(
8
)
−
1
Calculate
f
(
8
)
f(8)
f
(
8
)
:
Finally, we calculate
f
(
8
)
f(8)
f
(
8
)
.
\newline
f
(
8
)
=
−
3
(
8
)
−
1
f(8) = -3(8) - 1
f
(
8
)
=
−
3
(
8
)
−
1
\newline
f
(
8
)
=
−
24
−
1
f(8) = -24 - 1
f
(
8
)
=
−
24
−
1
\newline
f
(
8
)
=
−
25
f(8) = -25
f
(
8
)
=
−
25
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