Answer :
To find [tex]\( f(3) \)[/tex] for the function [tex]\( f(x) = \left(\frac{1}{9}\right)\left(g^x\right) \)[/tex], follow these steps:
1. Understanding the function: The function is given as [tex]\( f(x) = \left(\frac{1}{9}\right)\left(g^x\right) \)[/tex]. This means for any input [tex]\( x \)[/tex], you first raise [tex]\( g \)[/tex] to the power of [tex]\( x \)[/tex] (i.e., [tex]\( g^x \)[/tex]), then multiply the result by [tex]\(\frac{1}{9}\)[/tex].
2. Finding [tex]\( f(3) \)[/tex]: We need to calculate [tex]\( f(3) \)[/tex], which is substitution of [tex]\( x = 3 \)[/tex] into the function.
3. Assume a value for [tex]\( g \)[/tex]: Since the value of [tex]\( g \)[/tex] is not provided, let's assume it is a value that allows the completion of the problem, such as [tex]\( g = 9 \)[/tex].
4. Compute the exponential part [tex]\( g^3 \)[/tex]: Using our assumption [tex]\( g = 9 \)[/tex], calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
5. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Now, substitute back into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
6. Calculate the final result:
[tex]\[
f(3) = \frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\(\boxed{81}\)[/tex].
1. Understanding the function: The function is given as [tex]\( f(x) = \left(\frac{1}{9}\right)\left(g^x\right) \)[/tex]. This means for any input [tex]\( x \)[/tex], you first raise [tex]\( g \)[/tex] to the power of [tex]\( x \)[/tex] (i.e., [tex]\( g^x \)[/tex]), then multiply the result by [tex]\(\frac{1}{9}\)[/tex].
2. Finding [tex]\( f(3) \)[/tex]: We need to calculate [tex]\( f(3) \)[/tex], which is substitution of [tex]\( x = 3 \)[/tex] into the function.
3. Assume a value for [tex]\( g \)[/tex]: Since the value of [tex]\( g \)[/tex] is not provided, let's assume it is a value that allows the completion of the problem, such as [tex]\( g = 9 \)[/tex].
4. Compute the exponential part [tex]\( g^3 \)[/tex]: Using our assumption [tex]\( g = 9 \)[/tex], calculate [tex]\( 9^3 \)[/tex]:
[tex]\[
9^3 = 9 \times 9 \times 9 = 729
\][/tex]
5. Multiply by [tex]\(\frac{1}{9}\)[/tex]: Now, substitute back into the function:
[tex]\[
f(3) = \left(\frac{1}{9}\right) \times 729
\][/tex]
6. Calculate the final result:
[tex]\[
f(3) = \frac{729}{9} = 81
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] is [tex]\(\boxed{81}\)[/tex].
