Given that f(x) = x^{2}-2x+5 and g(x) =x+8, what is the value of f(g(5)) -g(f(5))?
+526 It is given that
\(f(x)=x^2-2x+5\)
\(g(x)=x+8\)
∴ \(g(5) = 5 + 8 \)
\(= 13\)
\(f(g(5)) = f(13) \)
\(= 169 - 2(13) + 5 \)
\(=148\)
Now,
\(f(5) = 25 - 10 +5\)
\(=20\)
\(g(f(5))=g(20)\)
\(= 20+8\)
\(=28\)
∴ \(f(g(5)) - g(f(5)) = 148-28\)
\(=120\)
+526 It is given that
\(f(x)=x^2-2x+5\)
\(g(x)=x+8\)
∴ \(g(5) = 5 + 8 \)
\(= 13\)
\(f(g(5)) = f(13) \)
\(= 169 - 2(13) + 5 \)
\(=148\)
Now,
\(f(5) = 25 - 10 +5\)
\(=20\)
\(g(f(5))=g(20)\)
\(= 20+8\)
\(=28\)
∴ \(f(g(5)) - g(f(5)) = 148-28\)
\(=120\)
