what is the domain of $f(x)=3^{x - 2}$?\n{$x|x > 0$}\n{$x|x < 0$}\n{$x|x = 0$}\n{$x|x$ is a real number}

Explanation:

Step1: Recall domain definition

The domain of a function is the set of all possible input - values (x - values).

Step2: Analyze the exponential function

The function $f(x)=3^{x - 2}$ is an exponential function of the form $y = a^{u}$, where $a = 3$ and $u=x - 2$. Exponential functions of the form $y=a^{x}$ ($a>0,a\neq1$) are defined for all real - valued exponents. There are no restrictions on the value of $x$ for which we can calculate $3^{x - 2}$. We can substitute any real number for $x$ into the function $f(x)=3^{x - 2}$.

Answer:

${x\mid x\text{ is a real number}}$