Find the domain by finding where the expression is defined.
Interval Notation:
Interval Notation: ( − ∞ , 2 3 ] (-∞,23]
Set-Builder Notation: { x ∣ ∣ ∣ x ≤ 2 3 }
Answer: (-∞ , 2/3)
Explanation:
To find the domain of a radical , we will set the function inside the radical greater than or equal to zero , that is
2 - 3x ≥ 0
2 ≥ 3x
2/3 ≥ x
that is : x ≤ 2/3
Also
5 - x ≥ 0
5 ≥ x
That is : x ≤ 5
Therefore , the domain of the expression is x ≤ 2/3 and x ≤ 5
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