How to find domain of complicated composite functions. Find the domain of arccos(e^x), are there universal steps I can take to be able to find the domain?

Mark Rosales

Mark Rosales

Answered question

2022-11-18

How to find domain of complicated composite functions. Find the domain of arccos( e x ), are there universal steps I can take to be able to find the domain?

Answer & Explanation

klofnu7c2

klofnu7c2

Beginner2022-11-19Added 14 answers

e x is defined everywhere, but for arccos ( t ) you want 1 t 1. Now e x > 0 > 1, but what do you need to get e x 1?
Alberto Calhoun

Alberto Calhoun

Beginner2022-11-20Added 5 answers

For f ( g ( x ) ) to make sense, one needs g ( x ) d o m ( f <mo stretchy="fal, so d o m ( f g ) = g 1 ( d o m ( f ) ). With f = arccos and g = exp, you have d o m ( f ) = [ 1 , 1 ] and d o m ( f g ) = g 1 ( [ 1 , 1 ] ) = ( , 0 ].

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