#domain of composite pair of functions

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fading skyBOT
junior crag
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<@&286206848099549185>

junior crag
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whatsup

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@junior crag

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ping me if help

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For f(x)=1/(x+3) , g(x)=1/(x-9) the domain of f(g(x)) would be (-inf,-3)U(-3,9)U(9,inf) right?

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@junior crag

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Just wondering if this is correct answer

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no because

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f has all domain except when x=3

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but x is now g

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so g cant be 3

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solve that and then u willl know the domain

junior crag
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but x is replaced with g

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so f is 1/(g+3)

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obviosuly g cant be -3

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but also x cant be -3

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because it was orginally undefined there

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So x=+3

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?

junior crag
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This is what I have for my work but I don’t know how to solve for f(g(x))

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you dont need f(g)

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unless it says so

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just plug in g for x

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Well the problem says to find the domain for f(g(x)

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When plugging in g in the problem for f(x) I get 1/((1/x-9)+3/1))

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@junior crag

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well so u have to account for domain of f without g, domain of g, and the domain breaks of f evaluate at g instead of x

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you dont even need f(g)

junior crag
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yea

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and all the places where domain of f is broken substitute for g as well after using nromal x

junior crag