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, multiply 9 by \( \frac{1}{81} \): \( 9\times\frac{1}{81}=\frac{9}{81} \). Simplify \( \frac{9}{81} \) by dividing numerator and denominator by 9: \( \frac{9\div9}{81\div9}=\frac{1}{9} \).

Answer:

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