What is the continuity of the composite function f(g(x)) given

Journey Stout 2022-01-22 Answered
What is the continuity of the composite function f(g(x)) given f(x)=1x and g(x)=x1
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Expert Answer

fumanchuecf
Answered 2022-01-23 Author has 21 answers
Explanation:
The process here is to verify first the domain of g(x) (the inner function in the composition).
The domain is {xx>1,xR}
f(g(x))=1x
There will be two types of restriction on the domain in this problem.
- When the number underneath the is less than 0.
- When the denominator equals 0.
The number under the square root will be negative whenever x<1. The denominator will equal 0 when x=1, so the domain of the composition is
{xx>1,xR}
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