Purchase Solution

Providing Proof about Functions

Not what you're looking for?

Ask Custom Question

Let f: X--> Y and g: Y-->Z be functions. Show that if g o f is injective, then f must be injective. Is it true that g must also be injective? Show that if g o f is surjective, then g must be surjective. Is it true that f must also be surjective?

Purchase this Solution
Solution Summary

This solution helps with proof about functions.

Solution Preview

Recall that a function f:X-->Y is called injective, if for any elements x and x' from X, the equality f(x)=f(x') implies that x=x'. f is called surjective if for any element y from Y there exists an element x from X such that f(x)=y.

Let gf: X-->Z be injective, and let x, x' be elements of X such that ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • diminishing marginal utility

    Now we start the proof. We first show that a diminishing marginal rate of substitution does not imply diminishing marginal utilities by providing a counter example.

  • Extrema and Rolle's theorem

    This solution shows how to locate and classify extrema of giving functions and use Rolle's theorem to formulate a proof about given continuous functions

  • Functions : Onto and One-to-one, Bijections and Function Composition 'f o g'

    Proof: (a) Let f(x)=(11/7)(x+2)+3 (b) let f(x)=lnx (c) let f(x)=3x Thank you for using Brainmass. This posting involves a problem about graphs and functions. Onto and One-to-one, Bijections and Function Composition are investigated.

  • Functions of Public Relations

    (source: http://www.bls.gov/oco/ocos086.htm ) Societal functions of a PR campaign are those functions which are aimed at providing benefits to the society in terms of providing them information about good and bad products, advantages and disadvantages

  • Functions of Public Relations

    (source: http://www.bls.gov/oco/ocos086.htm ) Societal functions of a PR campaign are those functions which are aimed at providing benefits to the society in terms of providing them information about good and bad products, advantages and disadvantages

  • organizational and societal functions of Public Relations

    Societal functions of a PR campaign are those functions which are aimed at providing benefits to the society in terms of providing them information about good and bad products, advantages and disadvantages of new products, product comparison, etc.

  • Functions of Public Relations

    (source: http://www.bls.gov/oco/ocos086.htm ) Societal functions of a PR campaign are those functions which are aimed at providing benefits to the society in terms of providing them information about good and bad products, advantages and disadvantages

  • Measurable function

    89896 Measurable Functions Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x. Please make sure to show the proof in both directions.

  • Proof of the Linear Independence of Exponential Functions

    A proof of the linear independence of exponential functions is provided The solution is detailed and well presented.

View More Related Solutions