Domain of a Function is a Set of Values under which the Function is defined or a Set of Values which satisfy the respective Function.
The Given Function is : f(x) = [tex]\frac{3}{\sqrt{2x + 10}}[/tex]
The Condition for Square Root to be defined is any Expression under it should be Greater than or Equal to Zero.
When Function is a Fraction, it Cannot be defined when the denominator becomes zero. Because when the denominator is zero, the fraction tends to ∞ (because anything divided by zero tends to ∞)
According to Above Conditions Described above, The Given Function is Definable only when the Expression which is under the Square Root is Greater than Zero.
⇒ 2x + 10 > 0
⇒ 2x > -10
⇒ x > -5
In Set Builder Form it is Expressed as { x | x > -5 }
