UPSC NDA I 2021 Mathematics Solved Paper

Concept:The domain of a function is the set of all real numbers for which the function is defined and gives a finite output.Explanation:The given function is $f(x) = 3^{x}$, which is an exponential function.An exponential function with a positive base (here $3 > 0$) is defined for every real number $x$.For any real $x$, the value of $3^{x}$ is always a finite positive real number.Thus, there is no restriction on $x$ — it can take any value from $-\infty$ to $\infty$.Hence, the domain is the entire set of real numbers.Answer:A. $(-\infty, \infty)$