How do you know when to use brackets or parenthesis in finding domain or range?

Question

h(x)= x^2 - 5

Answer 1

Parenthesis means that the value is included and brackets mean it is not. For example y = ln(x), the domain is (0,inf) since 0 is not included in the domain. If you have infinity in your domain or range then it is also a braket, as above. More examples:

y = x, domain x an element of (-inf,inf)

or y = 1/x where x is positive, domain x an element of (0,inf)

y = x where x >= 0, domain x an element of [0,inf)

In the example above h(x) = x^2 - 5

domain x an element of (-inf,inf)

range y an element of [-5,inf)

since x may assume any value and for the range, x^2 will have the smallest value if x = 0 and y will equal -5 thus the minimum of y is -5 or y >= -5 hence the parenthesis.

Answer 2

at the begining point for you to see

Answer 3

for example

(2,5) this says from 2 to 5 NOT including 2 and 5

(2,5) same thing as 2 < x < 5

if I said

[2, 5] this says from 2 to 5 INCLUDING 2 and 5

[2, 5] same as 2 ≤ x ≤ 5

For the problem you have...

domain is all reals, you'd write this as

(-∞, ∞)   you always use parentheses with infinity

the range is from -5 to infinity  

[-5, ∞)  bracket with -5 because you include -5

gve772: you have your definitions of parenthesis and bracket mixed up