If f: A  B
and g: B C
are both one-to-one functions, then g o
f is one-to-one. |
Composition of One-To-One
Functions
| If f: A B
and g: B C
are both one-to-one functions, then g o
f is one-to-one. |
| Example: | Let A = {1, 2, 3, 4}, B = {w, v, x, y, z} and C = {p, q, r, s, t, u}.
Then define a function f: AB
and g: BC
which are illustrated at the diagrams below.
Both f and g are one-to-one functions. Find g o f. |
| Solution: | g o f is shown
as
Clearly, the composition (g o f) is one-to-one. |
and 
