QuestionDetermine the domain of the function $m(t)=\sqrt{t-1}-3$ .

Studdy Solution

STEP 1

Assumptions1. The function is $m(t)=\sqrt{t-1}-3$ . We need to find the domain of this function3. The domain of a function is the set of all possible input values (t-values) which will produce a valid output4. For a square root function, the value inside the square root (the radicand) must be greater than or equal to zero, as we cannot take the square root of a negative number in the real number system

STEP 2

To find the domain, we need to set the radicand greater than or equal to zero and solve for t.
$t-1 \geq0$

STEP 3

Add1 to both sides of the inequality to isolate t.
$t \geq1$

STEP 4

The domain of the function $m(t)=\sqrt{t-1}-3$ is all real numbers greater than or equal to1.
The solution is $t \geq1$ .

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