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 Given f(x) = x^2−1/ 1−x
and g(x) = x + 2. Find and simplify f(g(2))−g(f(2)).

 Dec 15, 2019
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\(f(x)=\frac{x^2-1}{1-x}\)

\(g(x)=x+2\)

 

find and simplify:

f(g(2))-g(f(2)) 

 

well, let's start with 
f(g(2)) it is composite so the inside then the outside i.e let's start with g(2)

we know that:

g(x)=x+2

so, g(2)=2+2=4 

subsituite g(2) by 4 in f(g(2))

f(4) 

well we know that 
\(f(x)=\frac{x^2-1}{1-x}\)

\(f(4)=\frac{4^2-1}{1-4}=\frac{15}{-3}=-5\)

So we know that f(g(2))= -5 

Now let's do the same for g(f(2))

\(f(2)=\frac{3}{-1}=-3\)

\(g(-3)=-3+2=-1\)

so, g(f(2)) = -1

f(g(2))-g(f(2))= -5-(-1) = -5+1=-4 

 Dec 16, 2019

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