The question is: f(x)=x/x−1, g(x)=1/x, h(x)=x2−1. Find f o g o h and state its domain.

vballa15ei 2022-09-14 Answered
The question is:
f ( x ) = x x 1
g ( x ) = 1 x
h ( x ) = x 2 1
Find f g h and state its domain.
The answer the textbook states is that the domain is all real values of x, except ± 1 and ± 2 .
However surely the domain excludes 0 as well, since g ( 0 ) is undefined.
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Answers (2)

Maleah Lester
Answered 2022-09-15 Author has 12 answers
You're not inputting x into g, though. You're inputting h ( x ). So yes, g ( 0 ) is undefined, which means that whatever values of x makes h ( x ) = 0 is not part of the domain. That's why they exclude ± 1.

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metal1fc
Answered 2022-09-16 Author has 2 answers
h ( x ) = x 2 1 has a value for all R
g ( h ( x ) ) = 1 x 2 1 which does not have a value at x = ± 1
f ( g ( h ( x ) ) ) = 1 x 2 1 1 x 2 1 1 = 1 1 x 2 + 1 = 1 2 x 2 which does not have a value at x = ± 2
Hence the total domain is x R { ± 1 , ± 2 }

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