Let f(x) =-2x+7f(x)=−2x+7 and g(x) = -6x+3g(x)=−6x+3. What is f *gf⋅g and what is its domain?

1 Answer
Alan P.
Dec 26, 2015

Either color(red)(12x+1)12x+1 or color(blue)(12x^2-48x+21)12x2−48x+21
depending upon interpretation of f*gf⋅g

In either case the Domain is all Real values (RR)

Explanation:

Given
color(white)("XXX")f(x)=-2x+7
and
color(white)("XXX")g(x)=-6x+3

Possibility 1
If f*g is intended to mean f@g (i.e. f(g(x)))
then
color(white)("XXX")(f(g(x)) = -2(g(x))+7
color(white)("XXXXXXXX")=-2(-6x+3)+7
color(white)("XXXXXXXX")=12x-6+7
color(white)("XXXXXXXX")=12x+1
which is defined for all Real values of x
rarr Domain =RR

Possibility 2
If f*g is intended to mean f xx g
then
color(white)("XXX")f(x)xxg(x)=(-2x+7)xx(-6x+3)
color(white)("XXXXXXXXXX")= 12x^2-48x+21
which is defined for all Real values of x
rarr Domain =RR

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