Question

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

Answer 1

Answer: (-∞ , 2/3)

Step-by-step 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

Answer 2

Find the domain by finding where the expression is defined.

Interval Notation:

Interval Notation: ( − ∞ , 2 3 ] (-∞,23]

Set-Builder Notation: { x ∣ ∣ ∣ x ≤ 2 3 }