One-to-One Functions
Read this topicExplanations 4
- Let AAA and BBB be two sets. A function (also called map) f:A→Bf:A\rightarrow Bf:A→B is said to be injective, or one-one, if no two elements of AAA are mapped to the same elemen…
By Neelarnab Raha, Anusha Rahman
- One-to-One Functions In this lesson, we will understand the concept of one-to-one functions, which is also known as injective functions. Only one-to-one functions can have an in…
By Angela Yang, Gabi Slizewska, Anusha Rahman
- (Video) Injective Functions by learnifyable Follow along with the examples in this video from learnifyable.
By Anusha Rahman
- Functions can be classified as one-to-one or onto based on how their outputs relate to the range. One-to-One Functions A function is like a machine that takes an input and gives…
By Anusha Rahman
Problems 24
- Consider the two sets of integers X={1,2,…,2015,2016}X=\{1,2,\ldots,2015,2016\}X={1,2,…,2015,2016} and Y={1,2,…,1994,1995}Y=\{1,2,\ldots,1994,1995\}Y={1,2,…,1994,1995}. Does the…
- Let aaa and bbb be real numbers, and let f(x)=ax+bf(x)=ax+bf(x)=ax+b. Find all pairs (a,b)(a,b)(a,b) of real numbers such that f(f(x))=4x+3f(f(x))=4x+3f(f(x))=4x+3 for all real …
- Select all of the following tables which represent yyy as a function of xxx and are one-to-one.
- True or False\text{True or False}True or False === Linear functions are always injective.
- True or False\text{True or False}True or False === A linear function of the form y=ax+by=ax+by=ax+b, where aaa and bbb are real numbers and greater than zero, is always injective.
- True or False? All one-to-one functions are continuous over (−∞,∞)(-\infty,\infty)(−∞,∞).
- The full graph of a quadratic function, f(x)=x2f(x)=x^2f(x)=x2, is not one-to-one, and doesn't have an inverse. What can we change in the function to make it one-to-one?
- Let f(x)f(x)f(x) be a one-to-one function that includes the point (4,3)(4,3)(4,3). Which of the following points cannot be on the function? Select all that apply.
- True or False? Functions with an even degree (x2,x4,x6,x^2, x^4, x^6,x2,x4,x6, etc.) are always one-to-one.
- Sets AAA and BBB give a list of inputs in the left bubble and outputs in the right bubble. Select all true statements about these two sets.
- True or False Continuous functions that have both increasing and decreasing sections cannot be one-to-one.
- True or False\text{True or False}True or False === All strictly increasing continuous functions are one-to-one.
- Which of the following functions are one-to-one?
- Which of the following graphs are one-to-one?
- True or False\text{True or False}True or False === The graph that represents the height of a basketball sss seconds after being thrown in the air is one-to-one.
- True or False\text{True or False}True or False === The graph that represents your height at age yyy years is one-to-one.
- True or False\text{True or False}True or False === In a one-to-one function, the size of the domain must be greater than or equal to the size of the codomain.
- True or False\text{True or False}True or False === All rational functions of the form f(x)=1ax+bf(x) = \frac{1}{ax+b}f(x)=ax+b1 are one-to-one functions.
- The full graph of f(x)=(x−5)8f(x)=(x-5)^8f(x)=(x−5)8, is not one-to-one. What can we change in the function to make it one-to-one?
- Which of the following functions are one-to-one?
- Which of the colored functions graphed above are one-to-one?
- Which trigonometric functions are one-to-one?
- Which of the following describes the graph of the function for converting Kelvin to Fahrenheit, F=1.8(K−273)+32F=1.8(K-273)+32F=1.8(K−273)+32?
- Jonny is riding a rollercoaster that looks exactly like the picture above. The rollercoaster is going 100100100mph. Jonny throws his hands up and feels the wind in his face, but…