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Let’s check out your problem:
Given
f
(
x
)
=
−
x
2
+
2
x
f(x)=-x^{2}+2 x
f
(
x
)
=
−
x
2
+
2
x
, find
f
(
−
9
)
f(-9)
f
(
−
9
)
\newline
Answer:
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Math Problems
Algebra 2
Composition of linear and quadratic functions: find a value
Full solution
Q.
Given
f
(
x
)
=
−
x
2
+
2
x
f(x)=-x^{2}+2 x
f
(
x
)
=
−
x
2
+
2
x
, find
f
(
−
9
)
f(-9)
f
(
−
9
)
\newline
Answer:
Substitute
x
x
x
with
−
9
-9
−
9
:
To find
f
(
−
9
)
f(-9)
f
(
−
9
)
, we need to substitute
x
x
x
with
−
9
-9
−
9
in the function
f
(
x
)
=
−
x
2
+
2
x
f(x) = -x^2 + 2x
f
(
x
)
=
−
x
2
+
2
x
.
f
(
−
9
)
=
−
(
−
9
)
2
+
2
(
−
9
)
f(-9) = -(-9)^2 + 2(-9)
f
(
−
9
)
=
−
(
−
9
)
2
+
2
(
−
9
)
Calculate values:
Now, we calculate the square of
−
9
-9
−
9
and multiply it by
−
1
-1
−
1
, and then multiply
2
2
2
by
−
9
-9
−
9
.
f
(
−
9
)
=
−
81
−
18
f(-9) = -81 - 18
f
(
−
9
)
=
−
81
−
18
Add numbers:
Next, we add the two numbers together to find the value of
f
(
−
9
)
f(-9)
f
(
−
9
)
.
f
(
−
9
)
=
−
81
−
18
=
−
99
f(-9) = -81 - 18 = -99
f
(
−
9
)
=
−
81
−
18
=
−
99
More problems from Composition of linear and quadratic functions: find a value
Question
Find the inverse of the function.
y
=
x
+
3
y = x + 3
y
=
x
+
3
Write your answer in the form
a
x
+
b
ax + b
a
x
+
b
. Simplify any fractions.
y
=
y =
y
=
_____
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Posted 9 months ago
Question
Find
(
r
∘
s
)
(
x
)
(r \circ s)(x)
(
r
∘
s
)
(
x
)
.
\newline
r(x) =
3
3
3
x
\newline
s(x) =
2
2
2
x +
5
5
5
\newline
Write your answer as a polynomial in simplest form.
\newline
(
r
∘
s
)
(
x
)
=
(r \circ s)(x) =
(
r
∘
s
)
(
x
)
=
____
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Posted 1 year ago
Question
What is
(
f
+
g
)
(
x
)
(f + g)(x)
(
f
+
g
)
(
x
)
?
\newline
f
(
x
)
=
−
3
x
f(x) = -3x
f
(
x
)
=
−
3
x
\newline
g
(
x
)
=
3
x
+
1
g(x) = 3x + 1
g
(
x
)
=
3
x
+
1
\newline
\newline
Write your answer as a polynomial or a rational function in simplest form.
\newline
‾
\underline{\hspace{3cm}}
\newline
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Posted 1 year ago
Question
What is
(
f
∗
g
)
(
x
)
(f * g)(x)
(
f
∗
g
)
(
x
)
?
\newline
f
(
x
)
=
−
x
+
4
f(x) = -x + 4
f
(
x
)
=
−
x
+
4
\newline
g
(
x
)
=
4
x
g(x) = 4x
g
(
x
)
=
4
x
\newline
\newline
Write your answer as a polynomial or a rational function in simplest form.
\newline
‾
\underline{\hspace{3em}}
\newline
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Posted 1 year ago
Question
What is the domain of
(
f
g
)
(
x
)
\left(\frac{f}{g}\right)(x)
(
g
f
)
(
x
)
?
\newline
f
(
x
)
=
2
x
f(x) = 2x
f
(
x
)
=
2
x
\newline
g
(
x
)
=
−
5
x
+
3
g(x) = -5x + 3
g
(
x
)
=
−
5
x
+
3
\newline
Choices:
\newline
[
A]All real numbers
[\text{A]All real numbers}
[
A]All real numbers
\newline
[
B]All real numbers except
3
5
[\text{B]All real numbers except } \frac{3}{5}
[
B]All real numbers except
5
3
\newline
[
C]All real numbers except
−
3
5
[\text{C]All real numbers except } -\frac{3}{5}
[
C]All real numbers except
−
5
3
\newline
[
D]All real numbers except
5
3
[\text{D]All real numbers except } \frac{5}{3}
[
D]All real numbers except
3
5
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Posted 1 year ago
Question
Find the inverse of the function.
\newline
y =
−
3
x
-3x
−
3
x
\newline
Write your answer in the form
a
x
+
b
ax + b
a
x
+
b
. Simplify any fractions.
\newline
y = ______
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Posted 1 year ago
Question
Find
(
f
∘
g
)
(
0
)
(f \circ g)(0)
(
f
∘
g
)
(
0
)
.
\newline
f
(
x
)
=
6
x
f(x) = 6x
f
(
x
)
=
6
x
\newline
g
(
x
)
=
x
2
+
4
x
g(x) = x^2 + 4x
g
(
x
)
=
x
2
+
4
x
\newline
(
f
∘
g
)
(
0
)
=
(f \circ g)(0) =
(
f
∘
g
)
(
0
)
=
____
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Posted 1 year ago
Question
Find
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
.
\newline
f
(
x
)
=
x
2
+
5
f(x) = x^2 + 5
f
(
x
)
=
x
2
+
5
\newline
g
(
x
)
=
4
x
g(x) = 4x
g
(
x
)
=
4
x
\newline
Write your answer as a polynomial in simplest form.
\newline
(
f
∘
g
)
(
x
)
=
(f \circ g)(x) =
(
f
∘
g
)
(
x
)
=
______
Get tutor help
Posted 1 year ago
Question
Is
f
(
x
)
f(x)
f
(
x
)
the inverse function of
g
(
x
)
g(x)
g
(
x
)
?
\newline
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
\newline
g
(
x
)
=
−
4
x
g(x) = -4x
g
(
x
)
=
−
4
x
\newline
Choices:
\newline
[yes]
\text{[yes]}
[yes]
\newline
[no]
\text{[no]}
[no]
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Posted 1 year ago
Question
What is
(
f
∗
g
)
(
x
)
(f * g)(x)
(
f
∗
g
)
(
x
)
?
f
(
x
)
=
3
x
2
+
9
x
f(x) = 3x^2 + 9x
f
(
x
)
=
3
x
2
+
9
x
g
(
x
)
=
3
x
g(x) = 3x
g
(
x
)
=
3
x
Write your answer as a polynomial or a rational function in simplest form. ______
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Posted 9 months ago
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