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Let’s check out your problem:
f(x) = \begin{cases} -x
−
4
-4
−
4
& , & x<
3
3
3
\ x^
2
2
2
−
7
-7
−
7
& , &
3
3
3
\leq x \leq
10
10
10
\ \dfrac{
120
120
120
}{x}+
5
5
5
& , & x >
10
10
10
\end{cases} f(
4
4
4
)=
\newline
A)
9
9
9
\newline
B)
−
1
-1
−
1
\newline
C)
7
7
7
\newline
D)
16
16
16
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Math Problems
Precalculus
Compound interest: word problems
Full solution
Q.
f(x) = \begin{cases} -x
−
4
-4
−
4
& , & x<
3
3
3
\ x^
2
2
2
−
7
-7
−
7
& , &
3
3
3
\leq x \leq
10
10
10
\ \dfrac{
120
120
120
}{x}+
5
5
5
& , & x >
10
10
10
\end{cases} f(
4
4
4
)=
\newline
A)
9
9
9
\newline
B)
−
1
-1
−
1
\newline
C)
7
7
7
\newline
D)
16
16
16
Identify Function Piece:
Identify which piece of the function to use for
x
=
4
x = 4
x
=
4
.
\newline
Since
3
≤
4
≤
10
3 \leq 4 \leq 10
3
≤
4
≤
10
, we use
f
(
x
)
=
x
2
−
7
f(x) = x^2 - 7
f
(
x
)
=
x
2
−
7
.
Substitute x =
4
4
4
:
Substitute
x
=
4
x = 4
x
=
4
into
f
(
x
)
=
x
2
−
7
f(x) = x^2 - 7
f
(
x
)
=
x
2
−
7
.
\newline
f
(
4
)
=
4
2
−
7
f(4) = 4^2 - 7
f
(
4
)
=
4
2
−
7
Calculate Result:
Calculate
4
2
−
7
4^2 - 7
4
2
−
7
.
\newline
4
2
=
16
4^2 = 16
4
2
=
16
\newline
16
−
7
=
9
16 - 7 = 9
16
−
7
=
9
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