Find domain of fog, if 1. f(x)=x+5. g(x)=7/(x+7) 2. f(x)=sqrtx. g(x)=6x+18

Chesley

Chesley

Answered question

2021-09-09

Find domain of fog, if
1. f(x)=x+5.g(x)=7x+7
2. f(x)=x.g(x)=6x+18

Answer & Explanation

2abehn

2abehn

Skilled2021-09-10Added 88 answers

1. Replace x by g(x)f(x):
f(x)=x+5,g(x)=7x+7
(fog)(x)=f(g(x))=f(7x+7)
=7x+7+5
=7+5x+35x+7
(fog)(x)=5x+42x+7
x+7=0
x=7
Domain (fog)=(,7)(7,)
2. f(x)=x.g(x)=6x+18
(fog)(x)=f(g(x))
=f(6x+18)
=6x+18
(fog)(x)=f(g(x))
=6x+18
6x+180
6x18
x3
Domain (fog)=[3,)

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