Solving Linear Algebra: f(5x5+4x2+3) & 1-1 & Onto

In summary, the conversation is discussing some concepts in Linear Algebra, such as definitions and their importance in solving problems. The conversation also touches upon the concepts of 1-1 and onto functions and their meanings. These concepts are essential in understanding and solving problems in Linear Algebra.
  • #1
2slowtogofast
135
1
So in my linear class we are reveiwing some things befor we start working out of the book and i got this as a practice ?. I am confused on what is being asked and how to start off.


Let P5 be the set of all polynomials of degree 5 or less. Let p(x) be an element of P5 with p'(x) its derivitive. define function f as follows.

f: P5[tex]\rightarrow[/tex]P5

f(p(x))=xp'(x) + 1

a. find f(5x5+4x2+3)

b. is f 1 to 1 and explain

c. is f onto and explain
 
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  • #2
In Linear Algebra, you often have to start off with definitions themselves. Once you have the definitions in hand, the proofs become considerably easier.

What does 1-1 mean? What does onto mean? These are definitions. 1-1 means that f(x) = f(y) implies that x = y. This essentially means that no two unequal points in the domain map to the same point in the range. Onto means that every point in the range is taken up. For example, if we define f: R to R by f(x) = 2, then f is not onto because there is no point x0 in the domain such that f(x0) = 3, for instance. After you learn these definitions, the questions should be easy to answer.
 

Related to Solving Linear Algebra: f(5x5+4x2+3) & 1-1 & Onto

1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with linear equations and their representations in vector spaces. It involves the study of linear transformations, matrices, and systems of linear equations.

2. What does f(5x5+4x2+3) mean?

The notation f(x) is used to represent a function, where the input value is x and the output value is f(x). In this case, f(5x5+4x2+3) means that the function f is being applied to the expression 5x5+4x2+3.

3. How do I solve linear algebra problems?

To solve linear algebra problems, you need to have a good understanding of basic algebra and be familiar with concepts such as matrices, vectors, and systems of linear equations. It is also important to practice and work through problems step by step.

4. What does it mean for a function to be 1-1?

A function is 1-1 (or one-to-one) if each input value corresponds to a unique output value. This means that no two different inputs can result in the same output.

5. What is the significance of a function being onto?

A function is onto (or surjective) if every element in the output range is mapped to by at least one element in the input domain. In other words, the function covers the entire output range without any gaps.

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