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# Pre Calc

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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))

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