Question

Find domains of the following expressions.
sqrt(2-3x)+sqrt(5-x)

Answer 1

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

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