One-to-One Function Algebraic Method

Additional Resources:

In this lesson, we will delve into the process of determining whether a function is one-to-one algebraically. We have previously established that a function is considered one-to-one when each value of x corresponds to a unique value of y, and vice versa. Now, armed with this definition, we can construct a straightforward test. By evaluating f(a) and f(b), if we find that f(a) is equal to f(b), it implies that a must be equal to b for the function to maintain its one-to-one property. Consequently, we can substitute an 'a' value into the function as the input for x, and then substitute a 'b' value into the function as another input for x. If we set these two expressions equal to each other and subsequently deduce that a is indeed equal to b, it provides evidence that the function under examination is one-to-one.
One-to-One Function Algebraic Method:
YouTube - Video YouTube - Video
Text Lessons:
LibreTexts Analyze Math
+ Show More +