1 votes 1 votes Show that the function f(x) = ax + b from R->R is invertible, where a and b are constants, with a$\neq$0, and find the inverse of f How to check whether this function is onto? pls give a detailed solution Set Theory & Algebra kenneth-rosen discrete-mathematics functions set-theory&algebra + – aditi19 asked Nov 26, 2018 edited Mar 4, 2019 by Pooja Khatri aditi19 1.2k views answer comment Share Follow See all 8 Comments See all 8 8 Comments reply Magma commented Nov 26, 2018 reply Follow Share Inverse of f:A->B exists iff 'f' is a bijection 1) One-One f(x1) = f(x2) a(x1) + b = a (x2) + b x1 = x2 hence it's one-one function 2) Onto ax + b = c ax = b-c x = b - c / a given a !=0 I want to find out for every "C" there exists an element in domain or not therefore ,we can see that Yes for every value of 'C' we get the pre-image in Domain hence , it's Onto -function 1 votes 1 votes aditi19 commented Nov 26, 2018 reply Follow Share it'll be x=y-b /a right? 0 votes 0 votes Magma commented Nov 26, 2018 reply Follow Share aditi19 yeah but you ask in the question that How to check whether this function is onto? that'Y i just explain you one-one and onto 0 votes 0 votes Manas Mishra commented Nov 26, 2018 reply Follow Share @Magma inverse will be y-b/a right if take ax+b = y 0 votes 0 votes aditi19 commented Nov 26, 2018 reply Follow Share @Magma could you pls elaborate the onto part a little more? it's not clear to me 0 votes 0 votes Magma commented Nov 26, 2018 reply Follow Share y = ax+b x = ay+b x-b/a = y f-(x) = x -b /a 0 votes 0 votes Magma commented Nov 26, 2018 reply Follow Share onto mean : for every element in co-domain there should be a pre-image in domain right ?? now assume there's is an element in co-domain 'c' c is an arbitrary element now definitely element 'c' have pre-image in domain right ?? x = b - c / a now a and b are const it's given in the question and a ! =0 for any value of c we get the pre-image in domain you can check it now C can be any real number for every value in c we get pre-image in domain of the function 0 votes 0 votes aditi19 commented Nov 26, 2018 reply Follow Share oh! got it now... thanks 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes To find inverse of a function if inverse exits.. do this Put. f(x) = y ..........(1) f^-1(y)=x .......(2) In our case f(x) =ax+b =y ....... (3) Now put , x= f^-1(y) in (3) We have y = a.f^-1(y)+b (y-b)/a =f^-1(y) Puy x in place of y f^-1(x)=(x-b)/a this is the inverse of f(x) Kingdarab answered Aug 29, 2020 Kingdarab comment Share Follow See all 0 reply Please log in or register to add a comment.