Find the Domain and Range f(x) = square root of x^2+1-2

Set the radicand in ${\displaystyle \sqrt{x^2+1}}$ greater than or equal to ${\displaystyle 0}$ to find where the expression is defined.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

Set-Builder Notation:

The range is the set of all valid ${\displaystyle y}$ values. Use the graph to find the range.

Interval Notation:

Set-Builder Notation:

Determine the domain and range.

Domain: ${\displaystyle (-\infty ,\infty ),\left\{x\right|x\in ℝ\}}$

Range: ${\displaystyle [-1,\infty ),\left\{y\right|y\ge -1\}}$