Find the Composite Function

For
𝑓
(
𝑥
)
=
𝑥
and
𝑔
(
𝑥
)
=
3
𝑥
+
9
, find the following composite function.

Simplify your answer.

(
𝑓
∘
𝑔
)
(
𝑥
)
=

Question

Find the Composite Function

For 
𝑓
(
𝑥
)
=
𝑥
 and 
𝑔
(
𝑥
)
=
3
𝑥
+
9
, find the following composite function.

Simplify your answer.

(
𝑓
∘
𝑔
)
(
𝑥
)
=

BlackTom AI · Accepted Answer

We start by identifying the given functions: f(x) = x is the identity function, and g(x) = 3x + 9. When forming the composite (f ∘ g)(x), we apply g first and then f: (f ∘ g)(x) = f(g(x)).

Option by option analysis:
1) '3
x
+
9' — This matches the expression 3x + 9 if we interpret the line breaks as standard mathematical formatting. Since g(x) = 3x + 9 and f is the identity, applying f to g(x) leaves g(x) unchanged, yielding 3x + 9. This option is consistent with the definition of the composite in this problem.

2) '𝑥
4' — This would represent x^4 or x/4 depending on formatting; neither aligns with the calculated result, which must come from substituting g(x) into f and using f's identity property. This option misrepresents the composite and introduces an incorrect algebraic form.

3) '3
x
+
9' — This is a repetition of the first, just phrased with the same structure. Since the math leads to the same expression, this option also corresponds to the correct result, though it appears twice in the list. It's not introducing a new outcome beyond the first option, but it is mathematically the same as the correct composite result.

4) '9
x
+
36' — This would correspond to 9x + 36, which would arise if g(x) were scaled by 3 again or if there were a misapplication of the outer function, but f does not alter the coefficient or constant term beyond what g provides, and the identity f cannot change the linear combination in this way. Therefore, this option is inconsistent with the actual composition outcome.

In summary, the correct composite result is the expression obtained by substituting the inner function into the outer function and relying on f being the identity. The options that reproduce 3x + 9 are consistent with this result, while the others misrepresent the algebraic outcome or error in the composition process.

MAT-265-OD24-02-7799 Prior Knowledge Check

Find the Composite Function For 𝑓 ( 𝑥 ) = 𝑥 and 𝑔 ( 𝑥 ) = 3 𝑥 + 9 , find the following composite function. Simplify your answer. ( 𝑓 ∘ 𝑔 ) ( 𝑥 ) =

查看解析

登录即可查看完整答案

类似问题

Find the Following Values Given and , find the following values Simply your answer. [Fill in the blank] [Fill in the blank] [Fill in the blank]

State the Domain For f(x)= √ x and g(x)=3x+9, State the domain of (f∘g)(x)= Simply your answer.

Find the Composite Function For f(x)= √ x and g(x)=3x+9, find the following composite function. Simplify your answer. (f∘g)(x)=

State the Domain For 𝑓 ( 𝑥 ) = 𝑥 and 𝑔 ( 𝑥 ) = 3 𝑥 + 9 , State the domain of ( 𝑓 ∘ 𝑔 ) ( 𝑥 ) = Simply your answer.

Given the functions 𝑓 ( 𝑥 ) = 𝑥 2 + 4 𝑔 ( 𝑥 ) = 𝑥 − 1 𝑥 Then ( 𝑓 ∘ 𝑔 ) ( 𝑥 ) is equal to

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单