81. f(x) = 1 / (x² + 1)
81. f(x) = 1 / (x² + 1)
Answer
Explanation:
Step1: Identify the problem type
This is a function - related problem.
Step2: Analyze the function
The function is $f(x)=\frac{1}{x^{2}+1}$. There is no further simplification or specific operation requested in the given problem statement. If we assume we want to find the domain, since the denominator $x^{2}+1$ is always positive for all real - valued $x$ (because $x^{2}\geq0$ for all real $x$, so $x^{2}+1\geq1$), the domain of $f(x)$ is all real numbers, i.e., $(-\infty,\infty)$.
Answer:
Domain: $(-\infty,\infty)$