Questions: Compute the value of the function. f(x)=6 * (3^x) f(-2)=[?]

Compute the value of the function. f(x)=6 * (3^x) f(-2)=[?]
Transcript text: Compute the value of the function. \[ f(x)=6 \cdot\left(3^{x}\right) \quad f(-2)=[?] \]
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Solution

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Solution Steps

To solve for \( f(-2) \) in the function \( f(x) = 6 \cdot (3^x) \), we need to substitute \( x = -2 \) into the function and compute the result.

Step 1: Substitute \( x = -2 \) into the function

Given the function \( f(x) = 6 \cdot (3^x) \), we substitute \( x = -2 \): \[ f(-2) = 6 \cdot (3^{-2}) \]

Step 2: Simplify the exponent

Recall that \( 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \): \[ f(-2) = 6 \cdot \frac{1}{9} \]

Step 3: Perform the multiplication

Simplify the multiplication: \[ f(-2) = 6 \cdot \frac{1}{9} = \frac{6}{9} = \frac{2}{3} \approx 0.6667 \]

Final Answer

\(\boxed{\frac{2}{3}}\)

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