+318 Given f(x) = x^2−1/ 1−x
and g(x) = x + 2. Find and simplify f(g(2))−g(f(2)).
\(f(x)=\frac{x^2-1}{1-x}\)
\(g(x)=x+2\)
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
