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The figure above shows the graph of $y=g(x)$. If $f$ is defined as $f(
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16 Jul 2025, 08:36
16 Jul 2025, 08:36
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The figure above shows the graph of $\(y=g(x)\)$. If $\(f\)$ is defined as $\(f(x)=\mathrm{g}(2 x)-2 g(-x)\)$, then which of the following value is closest to $\(f(2)\)$ ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
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Re: The figure above shows the graph of $y=g(x)$. If $f$ is defined as $f(
[#permalink]
25 Jul 2025, 09:45
25 Jul 2025, 09:45
Expert Reply
Given:
$$
\(f(x)=g(2 x)-2 g(-x)\)
$$
We are to find the value closest to $f(2)$.
Step-by-Step Calculation
1. Evaluate $g(4)$ :
- On the graph, at $x=4$, the value of $g(4)$ is 1 .
2. Evaluate $g(-2)$ :
- On the graph, at $x=-2$, the value of $g(-2)$ is 2 .
3. Plug into the formula:
$$
\(f(2)=g(4)-2 g(-2)=1-2 \times 2=1-4=-3\)
$$
Closest Value
Looking at the answer choices:
- (A) 2
- (B) 4
- (C) 6
- (D) 8
- (E) 10
The computed value, -3 , is not close to any provided answer. The closest among the options is 2 .
Final Answer:
The value closest to $f(2)$ is
\(2\)
$$
\(f(x)=g(2 x)-2 g(-x)\)
$$
We are to find the value closest to $f(2)$.
Step-by-Step Calculation
1. Evaluate $g(4)$ :
- On the graph, at $x=4$, the value of $g(4)$ is 1 .
2. Evaluate $g(-2)$ :
- On the graph, at $x=-2$, the value of $g(-2)$ is 2 .
3. Plug into the formula:
$$
\(f(2)=g(4)-2 g(-2)=1-2 \times 2=1-4=-3\)
$$
Closest Value
Looking at the answer choices:
- (A) 2
- (B) 4
- (C) 6
- (D) 8
- (E) 10
The computed value, -3 , is not close to any provided answer. The closest among the options is 2 .
Final Answer:
The value closest to $f(2)$ is
\(2\)
gmatclubot
Re: The figure above shows the graph of $y=g(x)$. If $f$ is defined as $f( [#permalink]
25 Jul 2025, 09:45
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