https://www.quora.com/profile/Bravewarrior/p-147056235

Here is the question and its solution.I am basically stuck on how they got the domain in the solution. Could someone please explain that to me? Thanks!

Here is the question and its solution.I am basically stuck on how they got the domain in the solution. Could someone please explain that to me? Thanks!

Remember, informally, the domain is "what values can x take such that the function f(x) doesn't explode".

So really what it's asking is what values $3\cot^2(2t)$ can it be as t runs through 0 to pi/4.

Or, to make things a bit easier, it's the same as asking $3\cot^2(t)$ as t runs through 0 to pi/2.

The answer should be apparent if you sketch the graph of cot(t).

Remark: It's basically the same as finding the range of the function $f(t)=3\cot^2(2t), 0<t\leq \pi/4$. I just happen to call the function x instead of f. As with finding ranges, I think there are no shortcuts other than sketching the curve first.

So really what it's asking is what values $3\cot^2(2t)$ can it be as t runs through 0 to pi/4.

Or, to make things a bit easier, it's the same as asking $3\cot^2(t)$ as t runs through 0 to pi/2.

The answer should be apparent if you sketch the graph of cot(t).

Remark: It's basically the same as finding the range of the function $f(t)=3\cot^2(2t), 0<t\leq \pi/4$. I just happen to call the function x instead of f. As with finding ranges, I think there are no shortcuts other than sketching the curve first.

(edited 8 months ago)

Original post by tonyiptony

Remember, informally, the domain is "what values can x take such that the function f(x) doesn't explode".

So really what it's asking is what values $3\cot^2(2t)$ can it be as t runs through 0 to pi/4.

Or, to make things a bit easier, it's the same as asking $3\cot^2(t)$ as t runs through 0 to pi/2.

The answer should be apparent if you sketch the graph of cot(t).

Remark: It's basically the same as finding the range of the function $f(t)=3\cot^2(2t), 0<t\leq \pi/4$. I just happen to call the function x instead of f. As with finding ranges, I think there are no shortcuts other than sketching the curve first.

So really what it's asking is what values $3\cot^2(2t)$ can it be as t runs through 0 to pi/4.

Or, to make things a bit easier, it's the same as asking $3\cot^2(t)$ as t runs through 0 to pi/2.

The answer should be apparent if you sketch the graph of cot(t).

Remark: It's basically the same as finding the range of the function $f(t)=3\cot^2(2t), 0<t\leq \pi/4$. I just happen to call the function x instead of f. As with finding ranges, I think there are no shortcuts other than sketching the curve first.

Thank you so much!!! 🙂

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can someone please explain what principle domain is and why the answer is a not c?Maths

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