Question

H(x)=5/sqrt(2x+10), find the domain using set builder notation.

Answer 1

The given expression is

$h(x) = \frac{5}{\sqrt{2x+10}}$

THe given expression is a rational expression, and rational expression should not have 0 in the denominator.

Moreover, the denominator is a square root term, and square root don't have a value for negative number .

Therefore 2x+10 must be greater then 0. That is

$2x+10>0 \\ 2x>-10 \\ x>-5$

Therefore the required domain in set builder form is

{$x | x>-5$}