Find the domain of $$ \mathrm{f}(\mathrm{x}) $$. $$ f(x)=\sqrt{6 x-42} $$ Answer Attempt 1 out of 2 Answer Type: Interval

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UpStudy AI · Accepted Answer

To find the domain of the function $$ f(x) = \sqrt{6x - 42} $$, we need to ensure that the expression inside the square root is non-negative (since the square root of a negative number is not a real number).

**Step 1: Set the inside of the square root greater than or equal to zero.**

$$
6x - 42 \geq 0
$$

**Step 2: Solve for $$ x $$.**

$$
6x \geq 42
$$
$$
x \geq 7
$$

**Conclusion:**

The domain of $$ f(x) $$ consists of all real numbers $$ x $$ such that $$ x $$ is greater than or equal to 7.

**Domain in Interval Notation:**

$$
[7, \infty)
$$
The domain of $$ f(x) = \sqrt{6x - 42} $$ is all real numbers $$ x $$ where $$ x \geq 7 $$, which can be written as $$[7, \infty)$$.

Find the domain of .

Answer Attempt 1 out of 2
Answer Type:
Interval

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Find the domain of . Answer Attempt 1 out of 2 Answer Type: Interval