How do you find the domain of $h(x) = (2x^2 + 5 )/ (sqrt(x-2))$ ?

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Answer 1 · 2018-06-02T16:55:49

Domain: ${x|x>2}$ or in interval notation $(2, oo)$

$h(x) = (2x^2 + 5 )/ (sqrt(x-2))$

The domain is restricted by the radical; what is within it cannot be negative and the denominator; it cannot equal zero:

$x-2>=0$

$x>=2$

and

$sqrt(x-2) !=0$

$(sqrt(x-2))^2 !=0^2$

$x-2 !=0$

$x!=2$

put it together:

$x>2$

Domain: ${x|x>2}$ or in interval notation $(2, oo)$

How do you find the domain of h(x) = (2x^2 + 5 )/ (sqrt(x-2))h(x) = (2x^2 + 5 )/ (sqrt(x-2))?