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]
