Type this in LibreOffice Math:

f(x) = left lbrace matrix{
x^2        # {} # nitalic if # x < 0      ##
x^3        # {} # nitalic if # 0 <= x < 3 ##
x^2 over 2 # {} # nitalic if # x >= 3
} right none

newline
newline
newline

f(x) = left lbrace matrix{
x^2   # {} # nitalic if # x < 0      ##
x^3   # {} # nitalic if # 0 <= x < 3 ##
x^2/2 # {} # nitalic if # x >= 3
} right none

and you’ll get:

functions with cases

functions with cases