Functions: One-to-One Functions
A function f is defined as one-to-one if, for a and b are in the domain of f and f (a) = f (b), it follows a = b.
Example:
Show f (x) = 5x + 12 is a
one-to-one function
Solution:
Let a and b be real numbers with f (a) = f (b):
f (a) = 5a + 12
f (b) = 5b + 12
5a + 12 = 5b + 12
5a = 5b
a = b
∴ f (x) = 5x + 12 is a one-to-one function
f (a) = 5a + 12
f (b) = 5b + 12
5a + 12 = 5b + 12
5a = 5b
a = b
∴ f (x) = 5x + 12 is a one-to-one function
Related Topics: