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

Duncan Reed

Duncan Reed

Answered question

2022-01-23

What is the continuity of the composite function f(g(x)) given f(x)=1x6 and g(x)=x2+5

Answer & Explanation

fumanchuecf

fumanchuecf

Beginner2022-01-24Added 21 answers

The function f(g(x)) means to take g(x) and plug it into f(x).
So, if f(x)=1x6, then f(g(x))=f(x)=1g(x)6. Using g(x)=x2+5 this becomes f(g(x))=1(x2+5)61x21.
So, we want to examine the continuity of the function 1x21
The only real issue that may arise from this function is if we have a denominator that equals 0, since that is not possible. Setting the denominator to 0 to see when this occurs, that yields x21=0, so x2=1 so there are discontinuities at x=1 and x=1

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