Interval and Range

Hello,

I was wondering,

1.how do we find the range of a function w/o a calculator?
2. how do we know if its this bracket () or this bracket []? what will determine it.

Thanks

Quote:

---

Originally Posted by l flipboi l

1.how do we find the range of a function w/o a calculator?


Thanks

---

This is done by knowing the shape and nature of the function in question. Also knowing the domain will be helpful. Do you have an example of a function you require the range for?

Quote:

---

Originally Posted by l flipboi l

2. how do we know if its this bracket () or this bracket []? what will determine it.

Thanks

---

example

(0,5) means all numbers between 0 and 5 but not including 0 and 5.

[0,5] means all numbers between 0 and 5 including 0 and 5.

Yeah, I was trying to work out this problem g(x) = sqrt(16-x^4)...i found the domain to be x=+-2

but I could not figure out the range...

also, how would I know which bracket to use? in this case, since x cannot be -2 or +2 should I use () meaning not to include -2 or +2?

Quote:

---

Originally Posted by l flipboi l

Yeah, I was trying to work out this problem g(x) = sqrt(16-x^4)...i found the domain to be x=+-2

---

This is not completely correct, you need to solve

$\displaystyle 16-x^4\geq 0$

which gives you $\displaystyle -2\leq x \leq 2$ this can be written as $\displaystyle [-2,2]$ as both $\displaystyle -2$ and $\displaystyle 2$ will return a value for $\displaystyle g(x)$