Given that f(x) = x^{2}-2x+5 and g(x) =x+8, what is the value of f(g(5)) -g(f(5))?
+592 f(x) = x2 - 2x + 5
g(x) = x + 8
f(g(5)) - g(f(5))
= [(g(5))2 - 2(g(5)) + 5] - [(f(5)) + 8]
= [((5) + 8)2 - 2((5)) + 5] - [((5)2 - 2(5) + 5) + 8]
= [169 - 10 + 5] - [25 - 10 + 5 + 8]
= 164 - 28
= 136
