Determine whether each of the following functions is convex, concave, both, or neither over the domain specified.

(a) f1x1, x22! ln 1x12 + 20 ln 1x22 over x1, x2 7 0

(b) f1x2!x sin 1x2 over x  [0, 2p]

(c) f1x2!x1x - 222 over all x Ú 0

(d) f1x2! 1x - 824 + 132x over all x

(e) f1x1c. . x52!3x1 + 11x2 - x3 - 8x5 over all 1x1c. . x52

(f) f1x1, x22!21x1 + 63x2 over x1, x2 Ú 0

(g) f1x1, x22! max 5x1, x26 over all x1, x2

(h) f1x1, x22! min 513x1 - 2x2, - 1x2226 over all x1, x2

(i) f1x1, x22!10>1x1 - 401x2 over x1, x2 Ú 0

(j) f1x1, x22! ln [-31x122 - 91x222] - 10>x2 over x1, x2 7 0