Could someone please check my work

Define max (f, g) and min (f, g) as in Example 5.2. 11. Show that 1 . max ( f , 9 ) = = ( f + 9 ) + 715 - 91. Let f and g be functions from D to IR and define the functions max (f, g) and min (f, g) from D to R by max (f, g)(x) = max {f(x), 9(x)} , min (f, g)(x) = min {f(x), g(x)}. There are two cases to consider. Case one: Letf(x) > g(x) for some x E P. ( ) )nin max (f, g) = f and If - gl = f - g since f 2 9. , = ( f + 9 ) += 1f - 91 = = =(f + 9 ) + = ( f - 9 ) = = (f+ g + f - g) = ( 2f ) = f = max (f, g) Case two: f(x) f So , = ( f + 9 ) + 7 1f - 91 = = 2 ( 5 + 9 ) + 2 (9 - $ ) = = ( f+ g + g - f ) = = (29) = g = max (f, g)