Find composite of f and g:f = {(1, 1), (2, 4), (3, 4), (4, 3)} g = {(1

1.	Find composite of f and g:f = {(1, 1), (2, 4), (3, 4), (4, 3)} g = {(1, 1), (3, 27), (4, 64)}
Answer» f = {(1, 1), (2, 4), (3, 4), (4, 3)} g = {(1, 1), (3, 27), (4, 64)} f(1) = 1, g(1) = 1 f(2) = 4, g(3) = 27 f(3) = 4, g(4) = 64 f(4) = 3 (gof) (x) = g(f(x)) (gof) (1) = g(f(1)) = g(1) = 1 (gof) (2) = g(f(2)) = g(4) = 64 (gof) (3) = g(f(3)) = g(4) = 64 (gof) (4) = g(f(4)) = g(3) = 27 ∴ gof = {(1, 1), (2, 64), (3, 64), (4, 27)}

Find composite of f and g:f = {(1, 1), (2, 4), (3, 4), (4, 3)} g = {(1, 1), (3, 27), (4, 64)}

Answer»

f = {(1, 1), (2, 4), (3, 4), (4, 3)}

g = {(1, 1), (3, 27), (4, 64)}

f(1) = 1, g(1) = 1

f(2) = 4, g(3) = 27

f(3) = 4, g(4) = 64

f(4) = 3

(gof) (x) = g(f(x))

(gof) (1) = g(f(1)) = g(1) = 1

(gof) (2) = g(f(2)) = g(4) = 64

(gof) (3) = g(f(3)) = g(4) = 64

(gof) (4) = g(f(4)) = g(3) = 27

∴ gof = {(1, 1), (2, 64), (3, 64), (4, 27)}