Let $f (x) = x + 8$ $f(x) = x + 8$ and $g (x) = 3 x$ $g(x) = 3x$ , how do you find each of the compositions and domain and range?

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Answer 1 · 2016-10-22T17:33:29

The compositons are $f (g (x)) = 3 x + 8$ $f(g(x))=3x+8$ Domain ∈ $RR$ Range ∈ $RR$
and $g(f(x))=3x+24$ Domain ∈ $RR$ Range∈ $RR$

$f(x)=x+8$

$g(x)=3x$

Replace x by 3x in g(x)
$fog(x)= f(g(x))=f(3x)=3x+8$
the domain is $RR$
and the range $RR$

Replace x by (x+8) in g(x)
$gof(x)=g(f(x))=g(x+8)=3(x+8)=3x+24$
the domain is $RR$
and the range $RR$

You can see that $f(g(x))!=g(f(x))$

Let f(x) = x + 8f(x)=x+8f(x) = x + 8 and g(x) = 3xg(x)=3xg(x) = 3x, how do you find each of the compositions and domain and range?