Question
Functions f ()=and _ g6)= find the compositionpnd 4moiinAnswermlcnpossible Write the doman ISTIE [nteonotahone8 D/D Oini (O,D) [n,o)26) -QUD (D,O] [D,O)Amain ot f - & :")"(#-)"
functions f ()= and _ g6)= find the composition pnd 4moiin Answer mlcn possible Write the doman ISTIE [nteo notahone 8 D/D Oini (O,D) [n,o) 26) - QUD (D,O] [D,O) Amain ot f - & : ")"(#-)"
Answers
? Composition of Functions Find the functions $f \circ g$, $g \circ f$, $f \circ f$, and $g \circ g$ and their domains. $$ f(x)=\frac{2}{x}, \quad g(x)=\frac{x}{x+2} $$
The problem we have X squared plus three is RG function. We're gonna do something to it so that we get extra the fourth. That's six think square and then plus 20. So if we were to square it, that gives us a plus nine on the end. So we're gonna have to add an additional 11. So f of X function is just gonna be X squared because that's what we're doing to the G of X and then at 11 okay?
We're going to calculate various compositions of the functions of X is equal to six X minus five and g of X equals X over two. So first F, composed with G of X, by definition is equal to F of G of X. So we pluck in G of X to FX. Get that this is equal to six times X over two minus five, which is equal to three X minus five For the second equation. We want to be composed with that. That's equal to G of f of X by definition, so we like f of X into G get this is equal to six X minus five over to which is equal to three x minus 5/2. Next Afghan post with Quebec's by definition, is equal to F of f of X, so we block f of X into itself and get six times six X minus five minus five, which is equal to 36 x minus 30 minus five. So minus 35 lastly, decompose with G of X is equal to jean of G indexed by definition plucking G of X into itself. We get the people to X over two over to which is equal to X over for the domain, for each of these is all real numbers, just as it is for F N g of X.
We're going to calculate various compositions of F and G or F of X, is equal to X squared and D of Axity Goto X plus one and then find the domains. So after Buster D of X, by definition is able to G of X so plugging in g of X for f of X, this is equal to X plus one, I swear, which is equal to X squared plus two x plus one if you want to expand them. Next, we have decomposed with F of X, which by definition is equal to G oh f of X. So we plug in f of x two g of X, Get that this is equal to X squared plus one next F composed with F of X, by definition is able to f of f of X, we're flying f of X into itself and get that this is equal to X squared squared which is equal to X the fourth. Lastly, he calculated chief of those with thi of x which by definition is GFT of X, so plug g of X into itself and we get X plus one plus one, which is equal to X plus two. For each of these functions, the domain is all riel numbers
So that this question will have X minus 14 so we don't have a 14 year, but we can see that 14 is just to seven. So that's X minus seven minus seven. So that means we have to plug Jack's interviewer back. So that's G off G.