- #1
jdz86
- 21
- 0
Homework Statement
(a) Let f,g: [a,b] [tex]\rightarrow[/tex] [tex]\Re[/tex].
Define: f [tex]\vee[/tex] g(x) = max(f(x),g(x)), x[tex]\in[/tex] [a,b]
f [tex]\wedge[/tex] g(x) = min(f(x),g(x)), x[tex]\in[/tex] [a,b]
(b) Let [tex]f_{+}[/tex] = f[tex]\vee[/tex]0, [tex]f_{-}[/tex] = -(f[tex]\wedge[/tex]0)
Show that: f = [tex]f_{+}[/tex] - [tex]f_{-}[/tex]
abs value of f = [tex]f_{+}[/tex] + [tex]f_{-}[/tex]
Homework Equations
[tex]f_{+}[/tex], [tex]f_{-}[/tex] [tex]\geq[/tex] 0
The Attempt at a Solution
(a) f [tex]\vee[/tex] g(x) equals the supremum and infimum for f [tex]\wedge[/tex] g(x). Supremum would be "b" for both f and g, and infimum of both would be "a"??
(b) Lost with this one. It relates to the first question I know, but trying to put them together hasn't been working.