Answer :
We are given the function
[tex]$$
f\left(x_i\right)=\frac{1}{g} \cdot 9^{x^*}.
$$[/tex]
Assuming that the star in the exponent indicates that the exponent is the value of our input (i.e., [tex]$x_i = x^*$[/tex]) and that the constant [tex]$g$[/tex] is equal to 1, we can rewrite the function as
[tex]$$
f(x)=\frac{1}{1} \cdot 9^x = 9^x.
$$[/tex]
Now, to find [tex]$f(3)$[/tex] we substitute [tex]$x=3$[/tex]:
[tex]$$
f(3)=9^3.
$$[/tex]
Evaluating [tex]$9^3$[/tex]:
[tex]$$
9^3=9\cdot9\cdot9=81\cdot9=729.
$$[/tex]
Thus, the value of [tex]$f(3)$[/tex] is
[tex]$$
\boxed{729}.
$$[/tex]
[tex]$$
f\left(x_i\right)=\frac{1}{g} \cdot 9^{x^*}.
$$[/tex]
Assuming that the star in the exponent indicates that the exponent is the value of our input (i.e., [tex]$x_i = x^*$[/tex]) and that the constant [tex]$g$[/tex] is equal to 1, we can rewrite the function as
[tex]$$
f(x)=\frac{1}{1} \cdot 9^x = 9^x.
$$[/tex]
Now, to find [tex]$f(3)$[/tex] we substitute [tex]$x=3$[/tex]:
[tex]$$
f(3)=9^3.
$$[/tex]
Evaluating [tex]$9^3$[/tex]:
[tex]$$
9^3=9\cdot9\cdot9=81\cdot9=729.
$$[/tex]
Thus, the value of [tex]$f(3)$[/tex] is
[tex]$$
\boxed{729}.
$$[/tex]
