Answer:
a = 9, b = 3, c = 1
Step-by-step explanation:
Using the rules of exponents
[tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex] ⇒ [tex]a^{m}[/tex] = [tex]\frac{1}{a^{-m} }[/tex] and [tex]a^{0}[/tex] = 1
Given
f(x) = [tex](\frac{1}{3}) ^{x}[/tex], then
f(- 2) =[tex](\frac{1}{3}) ^{-2}[/tex] = [tex]\frac{1}{3^{-2} }[/tex] = 3² = 9 ⇒ a = 9
f(- 1) = [tex](\frac{1}{3}) ^{-1}[/tex] = [tex]\frac{1}{3^{-1} }[/tex] = [tex]3^{1}[/tex] = 3 ⇒ b = 3
f(0) = [tex](\frac{1}{3}) ^{0}[/tex] = 1
