Mathematics

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This question has been answered by 5 people and has an average rating of 4.00 (based on 1 rating)

Indiana Jones is exploring through the Pyramid of Petrification. After wandering through the dark corridors he finally came to hallway with 3 different exits. He then saw a large stone slab covered in mathematical insignia. It read:

To pass through unharmed you must solve this question. Your answer will show you your path and lead you to your fate.

If f(x) = and g(x) = , both defined by their natural domains, which of the following is the domain of f ◦ g?

If you think the answer is , Go back the way you came.

If you think the answer is , go down the left path.

If you think the answer is , go down the right path.

If you think the answer is not given, go through the door in this wall.

Indie stares at the wall, perplexed. He's not very good with functions. What path should he take?

no description

Alternatives

The contributor suggests C is the correct option
Option	Alternative	First answers	Confirmed answers
A	He should go back.	0 (0.00%)	0 (0.00%)
B	He should go down the left path.	1 (20.00%)	0 (0.00%)
C	He should go down the right path.	0 (0.00%)	1 (100.00%)
D	He should go through the door in the wall.	4 (80.00%)	0 (0.00%)

Explanation

The following explanation has been provided relating to this question:

This question requires some knowledge on functions, domains and trigonometry. First step, finding f(g(x)). Basically, we take our function sin(x) and we put in into or f(x) function, replacing . Then you'll have f(x) = . If you know a little about trigonometry, . Therefore, rearranging gives: . So now, we have , which is simply , and the domain of cos(x) = .

Therefore Indie must go down the right path.

Topics

The following topics have been indicated as being relevant to this question:

Domains, Trigonometry, Functions

Comments

There are 3 comments for this question (1 top-level comment and 2 replies)

Written: 8:19pm, 24 Apr	Author has: 435 points and 8 badges

This question is very interesting in the sense that it's kind of like a riddle but of a more mathematical nature. Really cool that you could come up with this question.

However, there's something wrong about the answer and explanation (correct me if I'm wrong);

The use of identity is clever but I think the answer should be so instead which is a complex number if we use this method. Am I right?

Another thing is the domain of the composite function should not be because we need to find the range of g(x) that intersects the domain of f(x). At least that's what I understand. Again correct me if I'm wrong.. :)

All in all, the idea of the question is definitely worth a praise. It's really cool! Great effort..

	Written: 8:01am, 27 Apr	Author has: 435 points and 8 badges
	I'm sorry. A little mistake in my comment above.. instead of a complex number.
	Written: 10:52pm, 27 Apr	Reply written by question author
	Got a little caught up in my own understanding, thanks for the help!
	Add a reply to this comment

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