MCS013 - Assignment 8(d)

A function is onto if and only if for every y$y$ in the codomain, there is an x$x$ in the domain such that f(x)=y$f(x)=y$.

So in the example you give, f:R→R,f(x)=5x+2$f:\mathbb{R}\to \mathbb{R},f(x)=5x+2$, the domain and codomain are the same set: R.$\mathbb{R}.$ Since, for every real number y∈R,$y\in \mathbb{R},$ there is an x∈R$x\in \mathbb{R}$ such that f(x)=y$f(x)=y$, the function is onto. The example you include shows an explicit way to determine which x$x$ maps to a particular y$y$, by solving for x$x$ in terms of y.$y.$ That way, we can pick any y$y$, solve for f′(y)=x$f^{\prime }(y)=x$, and know the value of x$x$ which the original function maps to that y$y$.

Side note:

Note that f′(y)=f−1(x)$f^{\prime }(y)=f^{-1}(x)$ when we swap variables. We are guaranteed that every function f$f$ that is onto and one-to-one has an inverse f−1$f^{-1}$, a function such that f(f−1(x))=f−1(f(x))=x$f(f^{-1}(x))=f^{-1}(f(x))=x$.

Assignment based viva for Descret mathematics MCS013 held on Sunday.

Lab incharge

Descrete Mathematics - 22 Nov 2015
timing between Lab session. 8am to 2pm

Viva MCS013, MCSL016, MCSL017

All will be on Sunday between lab session
bhari se bhari sankhya me aakar Ignou ko dhanya karen.

cheers
Akshay

Paper

MCS-011

MCS-012

MCS-013

MCS-014

MCS-015

MCS-011	Problem Solving and Programming	June 2015
MCS-012	Computer Organisation & Assembly Language Programming	June 2015
MCS-013	Discrete Mathematics	June 2015
MCS-014	Systems Analysis and Design	June 2015
MCS-015	Communication Skills	June 2015
MCSL-016  S1	Internet Concepts and Web Design	June 2015
MCSL-016  S2	Internet Concepts and Web Design	June 2015
MCSL-016  S3	Internet Concepts and Web Design	June 2015
MCSL-016  S4	Internet Concepts and Web Design	June 2015
MCSL-017  S1	C and Assembly Language Programming	June 2015
MCSL-017  S2	C and Assembly Language Programming	June 2015
MCSL-017  S3	C and Assembly Language Programming	June 2015
MCSL-017  S4	C and Assembly Language Programming	June 2015

Internet Concepts and Web Design	December 2014
MCSL-016  S2	Internet Concepts and Web Design	December 2014
MCSL-016  S3	Internet Concepts and Web Design	December 2014
MCSL-016  S4	Internet Concepts and Web Design	December 2014
MCSL-017  S1	C and Assembly Language Programming	December 2014
MCSL-017  S2	C and Assembly Language Programming	December 2014
MCSL-017  S3	C and Assembly Language Programming	December 2014
MCSL-017  S4	C and Assembly Language Programming	December 2014

Problem Solving and Programming	December 2014
MCS-012	Computer Organisation & Assembly Language Programming	December 2014
MCS-013	Discrete Mathematics	December 2014
MCS-014	Systems Analysis and Design	December 2014
MCS-015	Communication Skills	December 2014

Internet Concepts and Web Design	December 2014
MCSL-016  S2	Internet Concepts and Web Design	December 2014
MCSL-016  S3	Internet Concepts and Web Design	December 2014
MCSL-016  S4	Internet Concepts and Web Design	December 2014
MCSL-017  S1	C and Assembly Language Programming	December 2014
MCSL-017  S2	C and Assembly Language Programming	December 2014
MCSL-017  S3	C and Assembly Language Programming	December 2014
MCSL-017  S4	C and Assembly Language Programming	December 2014

Problem Solving and Programming	December 2014
MCS-012	Computer Organisation & Assembly Language Programming	December 2014
MCS-013	Discrete Mathematics	December 2014
MCS-014	Systems Analysis and Design	December 2014
MCS-015	Communication Skills	December 2014