math 3 10

x1 01 01 01 x1 01 01 01 f f(-1) A a A(-1) a f f(-1) A a A(-1) a x x x x1 λ x . sin (x+1) x sin (x+1) x1 xn expression-in-x1-xn lambda x1 xn expression-in-x1-xn x1 xn D expression-in-x1-xn restriction lambda x1 xn expression-in-x1-xn D fgh fgh fg x fgx (fg) x = f g x f f f f(-1) = id f domainf = R f codomainf = Q -1 1 imagesin = -11 x x0 0 x0 x x0 { x   if   x<0 0   if   x=0 x   if   x>0 0 x0 1 x1 x piecewise piece 0 ltx0 piece 1 gtx1 otherwise x ab a/b n n! a b a/b 235 max {2,3,5} y y 01 y3 max {y| y3 01 } ab min {a,b} x xB x2 min {x2| xB } 3 3 xy xy xyz x+y+z x3 x3 a b amodb ab ab n a an x root x 2 n a root a n