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Let’s check out your problem:
What is
(
q
∗
s
)
(
x
)
?
(q*s)(x) ?
(
q
∗
s
)
(
x
)?
\newline
q
(
x
)
=
5
x
+
2
q(x)=5x+2
q
(
x
)
=
5
x
+
2
\newline
s
(
x
)
=
−
4
x
+
5
s(x)=-4x+5
s
(
x
)
=
−
4
x
+
5
\newline
Write your answer as a polynomial or a rational function.
\newline
◻
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Home
Math Problems
Algebra 2
Composition of linear and quadratic functions: find an equation
Full solution
Q.
What is
(
q
∗
s
)
(
x
)
?
(q*s)(x) ?
(
q
∗
s
)
(
x
)?
\newline
q
(
x
)
=
5
x
+
2
q(x)=5x+2
q
(
x
)
=
5
x
+
2
\newline
s
(
x
)
=
−
4
x
+
5
s(x)=-4x+5
s
(
x
)
=
−
4
x
+
5
\newline
Write your answer as a polynomial or a rational function.
\newline
◻
Identify functions:
Identify the functions to be multiplied.
q
(
x
)
=
5
x
+
2
q(x) = 5x + 2
q
(
x
)
=
5
x
+
2
s
(
x
)
=
−
4
x
+
5
s(x) = -4x + 5
s
(
x
)
=
−
4
x
+
5
Multiply functions:
Multiply the functions
q
(
x
)
q(x)
q
(
x
)
and
s
(
x
)
s(x)
s
(
x
)
.
(
q
∗
s
)
(
x
)
=
(
5
x
+
2
)
(
−
4
x
+
5
)
(q*s)(x) = (5x + 2)(-4x + 5)
(
q
∗
s
)
(
x
)
=
(
5
x
+
2
)
(
−
4
x
+
5
)
Distribute terms:
Distribute each term in the first polynomial to each term in the second polynomial.
\newline
(
q
∗
s
)
(
x
)
=
5
x
∗
(
−
4
x
)
+
5
x
∗
5
+
2
∗
(
−
4
x
)
+
2
∗
5
(q*s)(x) = 5x*(-4x) + 5x*5 + 2*(-4x) + 2*5
(
q
∗
s
)
(
x
)
=
5
x
∗
(
−
4
x
)
+
5
x
∗
5
+
2
∗
(
−
4
x
)
+
2
∗
5
Simplify expression:
Simplify the expression by performing the multiplications.
\newline
(
q
∗
s
)
(
x
)
=
−
20
x
2
+
25
x
−
8
x
+
10
(q*s)(x) = -20x^2 + 25x - 8x + 10
(
q
∗
s
)
(
x
)
=
−
20
x
2
+
25
x
−
8
x
+
10
Combine like terms:
Combine like terms.
\newline
(
q
∗
s
)
(
x
)
=
−
20
x
2
+
17
x
+
10
(q*s)(x) = -20x^2 + 17x + 10
(
q
∗
s
)
(
x
)
=
−
20
x
2
+
17
x
+
10
More problems from Composition of linear and quadratic functions: find an equation
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
=
_____
Get tutor help
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
)
=
____
Get tutor help
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
Get tutor help
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
Get tutor help
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
Get tutor help
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 = ______
Get tutor help
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
)
=
____
Get tutor help
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]
Get tutor help
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. ______
Get tutor help
Posted 9 months ago
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