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The given function is:

\[
g(t) = \sqrt{t^2 + 1}
\]

### To find the domain of this function:
The domain of a square root function requires that the expression inside the square root must be **non-negative** (greater than or equal to zero). 

Here, the expression inside the square root is:

\[
t^2 + 1
\]

Since \(t^2\) is always non-negative (because squaring any real number results in a non-negative value), and adding 1 makes the expression strictly positive, we can conclude that:

\[
t^2 + 1 \geq 1
\]

Thus, \(t^2 + 1\) is always positive for all real numbers \(t\).

### Domain:
The function is defined for **all real values of \(t\)**. Therefore, the domain of the function is:

\[
(-\infty, \infty)
\]

### Do you want more details or have any questions about this problem?

Here are some related questions you might want to explore:
1. What is the range of the function \(g(t)\)?
2. How do you find the domain of a rational function?
3. What happens to the domain if there is a different expression inside the square root?
4. Can a square root function ever have negative values in its domain?
5. How does the graph of \(g(t) = \sqrt{t^2 + 1}\) look like?

**Tip:** Remember that square root functions are defined only for non-negative values inside the root. Always check what makes the expression inside the square root valid!

Find the domain of the function g(t) = √(t² + 1).

Learn how to find the domain of the square root function g(t) = √(t² + 1) by understanding key concepts in algebra and the properties of square root functions. This problem is suitable for students in Grades 9-12.

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