Math Problem Statement
Given that
f
(
x
)
3
x
2
+
5
x
+
7
and
g
(
x
)
3 x + 4 , determine each of the following. Make sure to fully simplify your answer.
(a)
(
f
∘
g
)
(
x
)
(b)
(
g
∘
f
)
(
x
)
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Function Composition
Polynomials
Formulas
f(g(x)) = f(3x + 4)
g(f(x)) = g(3x^2 + 5x + 7)
Expansion of (a + b)^2 = a^2 + 2ab + b^2
Theorems
Function Composition
Suitable Grade Level
Grades 10-12
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