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Etho_x

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random question - how do you type in maths notation? Is there a website or software to switch from maths and natural input?
It's Latex. Personally I don't know how to use it yet but there is an option on the toolbar in the text box, denoted by "f(x)".
 

Etho_x

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How would I find the domain for this?
Recall that the domain of arctan x is all real x. However, for this question you have a restriction, that is the domain of sqrt(x^2 - 1).

For the function y = sqrt(x^2 - 1), the domain is that x >= 1, or x <= -1. Since the domain of arctan x is all real x, the domain of sqrt(x^2 - 1) is the domain of arctan(sqrt(x^2 - 1)), that is x >= 1, or x <= -1.
 

carrotsss

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random question - how do you type in maths notation? Is there a website or software to switch from maths and natural input?

 

Anaya R

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Actually that guide is a bit outdated.
I'm currently learning how to do LaTeX, so I'd recommend their website:
 

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Recall that the domain of arctan x is all real x. However, for this question you have a restriction, that is the domain of sqrt(x^2 - 1).

For the function y = sqrt(x^2 - 1), the domain is that x >= 1, or x <= -1. Since the domain of arctan x is all real x, the domain of sqrt(x^2 - 1) is the domain of arctan(sqrt(x^2 - 1)), that is x >= 1, or x <= -1.
So essentially is the domain of the composite function inside brackets transferred into the whole function?
 

Etho_x

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So essentially is the domain of the composite function inside brackets transferred into the whole function?
Yeah, but that’s only because the parent function (arctan x) has a domain of all real x. If it was a function like arccos x with a domain between -1 and 1 inclusive, I think there would be those restrictions which you’d have to consider.
 

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I'm late but how did u find the domain and range for the second question? And the range for the first
Range for 1st: using composite function again (let u=sqrtx^2-1) therefore, y=arctanu- find common restriction for 'u' and use both graphs to using the restriction to determine range and Domain
 

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