问题


There is a single choice question about high school mathematics. Answer the question by replying A, B, C or D.
Question: If f(x) = 3x, g(x) = 5x + 3, and h(x) = 1 – x^2, then f(g(h(x)))=
A. 15x^2 + 15
B. –15x^2 + 18
C. –15x^2 + 24
D. –225x^2 + 90x – 8
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

To find f(g(h(x))), we need to start from the innermost function and work our way out.

First, we evaluate h(x) = 1 - x^2.

Next, we plug h(x) into g(x) = 5x + 3, so g(h(x)) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = 8 - 5x^2.

Finally, we plug g(h(x)) into f(x) = 3x, so f(g(h(x))) = 3(8 - 5x^2) = 24 - 15x^2.

Therefore, the correct answer is:

C. -15x^2 + 24		 C
deepseekr1

To determine \( f(g(h(x))) \), start by evaluating the innermost function \( h(x) = 1 - x^2 \). Substitute \( h(x) \) into \( g(x) = 5x + 3 \):

\[
g(h(x)) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = -5x^2 + 8.
\]

Next, substitute \( g(h(x)) = -5x^2 + 8 \) into \( f(x) = 3x \):

\[
f(g(h(x))) = 3(-5x^2 + 8) = -15x^2 + 24.
\]

Comparing this result with the options, the correct answer is **C. \(-15x^2 + 24\)**.

**Answer: C**		 C
gpto1 C C
GPT-4o To determine \( f(g(h(x))) \), we need to work through the functions step by step:

1. First, find \( h(x) \):
\[
h(x) = 1 - x^2
\]

2. Next, substitute \( h(x) \) into \( g(x) \):
\[
g(h(x)) = g(1 - x^2) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = 8 - 5x^2
\]

3. Finally, substitute \( g(h(x)) \) into \( f(x) \):
\[
f(g(h(x))) = f(8 - 5x^2) = 3(8 - 5x^2) = 24 - 15x^2
\]

So, the correct answer is:
\[
C. -15x^2 + 24
\]

Therefore, the answer is C.		 C
llama3.1-70B-Instruct

B		 C
llama3.1-405B-Instruct

To find f(g(h(x))), we need to start from the innermost function and work our way out.

First, we have h(x) = 1 - x^2.

Next, we have g(h(x)) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = 8 - 5x^2.

Finally, we have f(g(h(x))) = 3(8 - 5x^2) = 24 - 15x^2.

So, the correct answer is C. -15x^2 + 24.		 C
DeepSeek-Coder-V2 B. –15x^2 + 18 C
Qwen2-72B-Instruct D. –225x^2 + 90x – 8 C
baichuan4 To solve this problem, we need to compose the functions f, g, and h together.

First, let's find h(x):
h(x) = 1 - x^2

Next, we find g(h(x)):
g(h(x)) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = 8 - 5x^2

Finally, we find f(g(h(x))):
f(g(h(x))) = 3(8 - 5x^2) = 24 - 15x^2

So the answer is C. –15x^2 + 24.		 C
doubao First find h(x) = 1 - x^2, then g(h(x)) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = 8 - 5x^2. Finally, f(g(h(x))) = 3(8 - 5x^2) = 24 - 15x^2. So the answer is C. C
minimax To find f(g(h(x))), we need to apply the functions in the order given, starting with h(x).

First, we apply h(x) = 1 – x^2:

h(x) = 1 – x^2

Next, we apply g(x) to h(x), which means we substitute h(x) into g(x):

g(h(x)) = g(1 – x^2) = 5(1 – x^2) + 3 = 5 – 5x^2 + 3 = 8 – 5x^2

Now, we apply f(x) to g(h(x)), which means we substitute g(h(x)) into f(x):

f(g(h(x))) = f(8 – 5x^2) = 3(8 – 5x^2) = 24 – 15x^2

Therefore, the correct answer is:

C. –15x^2 + 24		 C
kimi To solve the problem, we need to evaluate the composition of the functions f(g(h(x))) step by step.

1. First, find h(x): h(x) = 1 - x^2
2. Then, find g(h(x)): g(x) = 5x + 3, so g(h(x)) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = 8 - 5x^2
3. Finally, find f(g(h(x))): f(x) = 3x, so f(g(h(x))) = 3(8 - 5x^2) = 24 - 15x^2

So the correct answer is:
A. 15x^2 + 15
B. –15x^2 + 18
C. –15x^2 + 24
D. –225x^2 + 90x – 8

The correct answer is C. –15x^2 + 24.		 C
wenxinyiyan 首先，我们计算内层函数h(x)的值：
$h(x) = 1 - x^{2}$

接下来，将h(x)的值代入到g(x)中，得到g(h(x))：
$g(h(x)) = g(1 - x^{2}) = 5(1 - x^{2}) + 3 = 5 - 5x^{2} + 3 = - 5x^{2} + 8$

最后，将g(h(x))的值代入到f(x)中，得到f(g(h(x)))：
$f(g(h(x))) = f(- 5x^{2} + 8) = 3(- 5x^{2} + 8) = - 15x^{2} + 24$

所以，答案是C. $-15x^{2} + 24$。		 C
zhipu To find \( f(g(h(x))) \), we need to apply the functions step by step.

1. **First, find \( h(x) \):**
\[
h(x) = 1 - x^2
\]

2. **Next, find \( g(h(x)) \):**
\[
g(h(x)) = g(1 - x^2) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = 8 - 5x^2
\]

3. **Finally, find \( f(g(h(x))) \):**
\[
f(g(h(x))) = f(8 - 5x^2) = 3(8 - 5x^2) = 24 - 15x^2
\]

So, \( f(g(h(x))) = 24 - 15x^2 \).

The correct answer is:
C. –15x^2 + 24

Answer: C		 C
gpto1 C C
deepseekv3 To solve \( f(g(h(x))) \), we need to substitute step by step:

1. **Calculate \( h(x) \):**
\[
h(x) = 1 - x^2
\]

2. **Substitute \( h(x) \) into \( g(x) \):**
\[
g(h(x)) = 5(1 - x^2) + 3 = 5 - 5x^2 + 3 = 8 - 5x^2
\]

3. **Substitute \( g(h(x)) \) into \( f(x) \):**
\[
f(g(h(x))) = 3(8 - 5x^2) = 24 - 15x^2
\]

The final expression is \( -15x^2 + 24 \).

**Answer:** C		 C