Question

use the function below to find ( f(-2) ).( f(x) = 3^x )a. -6b. ( \frac{1}{9} )c. ( \frac{1}{6} )d. -9

Explanation:

Step1: Substitute \( x = -2 \) into \( F(x) \)

We have the function \( F(x) = 3^x \). To find \( F(-2) \), we substitute \( x = -2 \) into the function, so we get \( F(-2) = 3^{-2} \).

Step2: Apply the negative exponent rule

The negative exponent rule states that \( a^{-n} = \frac{1}{a^n} \) for any non - zero number \( a \) and positive integer \( n \). Using this rule for \( 3^{-2} \), we have \( 3^{-2}=\frac{1}{3^2} \).

Step3: Calculate \( 3^2 \)

We know that \( 3^2=3\times3 = 9 \). So \( \frac{1}{3^2}=\frac{1}{9} \).

Answer:

B. \( \frac{1}{9} \)