How Do You Find F O G X And Its Domain G O F X And Its Domain F O G 2 And G O F

/in /by

Given##color(white)(“XXX”)f(color(blue)(x))=color(blue)(x)^2-1##and##color(white)(“XXX”)g(color(red)(x))=color(red)(x)+1##

Note that ##(f@g)(x)## can be written ##f(g(x))## and that ##(g@f)(x)## can be written ##g(f(x))##

##(f@g)(x) = f(color(blue)(g(x))) = color(blue)(g(x))^2-1####color(white)(“XXXXXX”)=(color(blue)(x+1))^2-1####color(white)(“XXXXXX”)=x^2+2x##Since this is defined for all Real values of ##x##,the of ##(f@g)(x)## is all Real values.(although it wasn’t asked for, the would be ##[-1,+oo)##)

Similarly##(g@f)(x)=g(color(red)(f(x)))+1####color(white)(“XXXXXX”)=g(color(red)(x^2-1))####color(white)(“XXXXXX”)=color(red)(x^2-1)+1####color(white)(“XXXXXX”)=x^2##Again, this is defined for all Real values of ##x##so the Domain is all Real values.(but the Range is ##[0,+oo)##)

 
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