Given f(x) = x^2, g(x) = x + 7 Find (f @ g)(x). Find the domain of (f @ g)(x). Find (g @ f)(x). Find the domain of (g @ f)(x). Find (f @ f)(x). Find the domain of (f @ f)(x). Find (g @ g)(x). Find the domain of (g @ g)(x).

FobelloE 2020-10-21 Answered
Given
f(x)=x2,g(x)=x+7
Find (fg)(x).
Find the domain of (fg)(x).
Find (gf)(x).
Find the domain of (gf)(x).
Find (ff)(x).
Find the domain of (ff)(x).
Find (gg)(x).
Find the domain of (gg)(x).
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Expert Answer

BleabyinfibiaG
Answered 2020-10-22 Author has 118 answers
fg(x)=f(g(x))=(g(x))2=(x+7)2
=x2+14x+49
It is a polunomial so domain is all real numbers
Domain of fg(x) is (,)
gf(x)=f(x)+7=x2+7
It is a polunomial so domain is all real numbers
Domain of gf(x) is (,)
ff(x)=(f(x))2=(x2)2=x4
It is a polunomial so domain is all real numbers
Domain of ff(x) is (,)
gg(x)=g(x)+7=x+7+7=x+14
It is a polunomial so domain is all real numbers
Domain of gg(x) is (,)
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