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Find [tex]\( f(-2) \)[/tex] for [tex]\( f(x) = 2 \cdot 3^x \)[/tex].

A. 1

Sagot :

GinnyAnswer
To solve for [tex]\( f(-2) \)[/tex] given the function [tex]\( f(x) = 2 \cdot 3^x \)[/tex]:

1. Substitute [tex]\( x = -2 \)[/tex] into the function:

[tex]\[ f(x) = 2 \cdot 3^x \][/tex]

So,

[tex]\[ f(-2) = 2 \cdot 3^{-2} \][/tex]

2. Simplify the exponent:

Recall that [tex]\( 3^{-2} \)[/tex] means [tex]\( \frac{1}{3^2} \)[/tex], which simplifies to [tex]\( \frac{1}{9} \)[/tex].

[tex]\[ 3^{-2} = \frac{1}{9} \][/tex]

3. Multiply by the constant 2:

[tex]\[ f(-2) = 2 \cdot \frac{1}{9} = \frac{2}{9} \][/tex]

4. Convert the fraction to its decimal form:

[tex]\( \frac{2}{9} = 0.2222222222222222 \)[/tex]

Thus,

[tex]\[ f(-2) = 0.2222222222222222 \][/tex]

Therefore, the solution is:

[tex]\( \boxed{0.2222222222222222} \)[/tex]
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