Answer:
[tex]f(3) = 3^{-2} = \frac{1}{3^{2}}[/tex] or [tex]\frac{1}{9}[/tex].
Step-by-step explanation:
Given the exponential function, [tex]f(x) = 3^{(1 - x)}[/tex], we can find f(3) by substituting the value of the input, x = 3, into the function.
[tex]f(x) = 3^{(1 - x)}[/tex]
[tex]f(3) = 3^{(1 - 3)} = 3^{(-2)}[/tex]
Hence, [tex]f(3) = 3^{-2}[/tex].
We can leave the final answer as [tex]f(3) = 3^{-2}[/tex]; however, it is more common to write exponential expressions with positive exponents. In order to transform the current exponential expression into a positive exponent, we can use the Negative Exponent Rule, where it states: [tex]a^{-n} = \frac{1}{a^{n} }[/tex].
Therefore, the correct answer is: [tex]f(3) = 3^{-2} = \frac{1}{3^{2}}[/tex] or [tex]\frac{1}{9}[/tex].
