Question

question 13 of 25
find ( f(-4) ) for ( f(x) = 9(3)^x ).

a. ( \frac{1}{9} )
b. ( -108 )
c. ( -729 )
d. ( \frac{1}{3} )

Explanation:

Step1: Substitute x = -4 into f(x)

We have the function \( f(x) = 9(3)^x \). To find \( f(-4) \), we substitute \( x = -4 \) into the function: \( f(-4)=9(3)^{-4} \).

Step2: Use the negative exponent rule

Recall the negative exponent rule: \( a^{-n}=\frac{1}{a^n} \). So, \( 3^{-4}=\frac{1}{3^4} \). Calculate \( 3^4 = 81 \), so \( 3^{-4}=\frac{1}{81} \).

Step3: Multiply by 9

Now, \( f(-4)=9\times\frac{1}{81} \). Simplify this fraction: \( \frac{9}{81}=\frac{1}{9} \).

Answer:

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