Use the Table to evaluate each expression.

x | 1 2 3 4 5 6

f | 3 1 4 2 2 5

g | 6 3 2 1 2 3

a). f (g (1))

b). g (f (1))

c). f (f (1))

d). g (g (1))

e). (gof) (3)

f). (fog) (6)

First we should know the general rule concerning the composition of functions For example, fog (x) = f[g (x) ] and gof (x) = g[f (x) ] a). f (g (1)) can be evaluated as follow: f (g (1)) = f[6]=5, because g (1) = 6 and f (6) = 5 b). g (f (1)) can be evaluated as follow: g (f (1)) = g (3) = 3 because f (1) = 3 and g (3) = 3 c). f (f (1)) can be evaluated as follow: f (f (1)) = f[3]=4, because f (1) = 3 and f (3) = 4 d). g (g (1)) can be evaluated as follow: g (g (1)) = g (6) = 3 because g (1) = 6 and g (6) = 3 e). (gof) (3) can be evaluated as follow: g (f (3)) = g (4) = 1 because f (3) = 4 and g (4) = 1 f). (gof) (6) can be evaluated as follow: g (f (6)) = g (3) = 2 because f (6) = 3 and g (3) = 2