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Let fx) = x + 2ad g(x) = 5x2 + x + 1.(a) Find (f 0 g)(x)(b) Find (g f(x).Submit Answer...

Question

Let fx) = x + 2ad g(x) = 5x2 + x + 1.(a) Find (f 0 g)(x)(b) Find (g f(x).Submit Answer

Let fx) = x + 2ad g(x) = 5x2 + x + 1. (a) Find (f 0 g)(x) (b) Find (g f(x). Submit Answer



Answers

Find $g \circ f$ and $f^{\circ} g$ for the given functions $f$ and $g .$ $$f(x)=\frac{2}{x+1}, \quad g(x)=3 x-5$$

So we're given that f of X is equal to two X minus one over X minus two. No, we're given that G of X is equal to X plus four over two X minus five and rats to find f of G gff after Beth and G. M G. So find f of G. We're going to be plugging in G of X and everywhere. There's an accident so that will give to of explosives for over two X minus five minus one over X plus four over two X minus five minus two. Doing the same thing for G of f. So plugging f into everywhere there's an X and G. We'll give two X minus one over X plus X minus two plus four over the same thing two X minus one over X minus two, multiplied by two minus five and then for af of off the plug F into everywhere, there's next enough, which is going to be too Times X minus one over X minus two minus one. All over. That's right. Two X minus one All over to X minus one over X minus two. Finest, too. And then finally Fergie remember, you the same thing. We will get X plus four over two X minus five plus four all over Teoh X plus four all over two X minus five minus five. So to simplify f of G, we're gonna be multiplying by two X minus fine and simplifying and doing so together, this equal 13 overnight of three x plus 14 Doing the same with gox, multiplying by X plus y g of f of x, Most number X minus two will give six X minus nine over negative experts. Eight. I guess nine. With FF multiple it multiply my X minus two. This gives three x over three, which is equal to X. I am doing this seemingly G of X multiply by two x minus five. Gives nine x when a 16 over negative eight x plus 33 so F of G is 13 over negative. Three expose 14 GFS six x minus nine over negative X plus eight f of f is x and g of x is nine x minus 16 and her negative file X plus 33

Were given the function F of X and G Fx. And we need to find G. F of X and F of G of X. So for the first one we're going to take a Fedex and plug it in in all the exes and G Fx. So we have negative five parentheses. So instead of X we're going to replace it with X. To the third power plus two X. So this simplifies to be negative five x cubed minus 10 X. For the second one. We're going to replace all the exes and F of X with G. FX. So this becomes X to the third power plus two times X. So we're gonna replace negative five X. Here. A negative five X. Here. So this simplifies negative 5 to the third power, oops negative five to the third power positive third car that's negative 125 X cubed. And then two times negative five is negative 10 X.

Given a full fix is do excess Quit minus X minus Lee and deal fixes. Nothing went explosive. Close t fix it is Do it for fix Close to your fix we can light this. Two extra square minus six minus three plus X plus one. This can be sold US two X squared minus two. No If blessed t fight, there's two into five square minus. True this to window 25 miners that is a 50 miners to

Given it all fixed is equal to four explosion India If X is equal to X minus night if blood t well thanks is nothing what it will fix. Plus deal fixed. It is four x plus two plus two weeks minus night. That is nothing but 66 minus seven. No, you have to solve for a full 50 off fight. That does not anybody off. I blessed you. Fight had this six into five minus seven. So that is 30 minus seven. That would go.


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