Question

122
course
ap precalculus
due tue, oct 7, 2025
6
default gallery

1. $x^{2}+1>0$

text math set matrix
answer

Explanation:

Step1: Analyze the property of $x^{2}$

For any real - number $x$, $x^{2}\geq0$.

Step2: Add 1 to both sides of the inequality for $x^{2}$

If $x^{2}\geq0$, then $x^{2}+1\geq0 + 1$, so $x^{2}+1\geq1$.
Since $1>0$, for all real numbers $x$, $x^{2}+1>0$.
The solution set is all real numbers, which can be written in interval notation as $(-\infty,\infty)$.

Answer:

The solution set is $(-\infty,\infty)$