321 views
0 votes
0 votes

Given that the function f and g ,  fog is composition of function,

also f and fog is one-to-one functions ,

then what can be said about ?

A) g is one-to-one function

B)can't say anything about g

1 Answer

0 votes
0 votes
If suppose g is not one-one then for x1!=x2 we have g(x1)=g(x2)=b

 Now as f is one-one f(b)=f(b) -> f(g(x1))=f(g(x2)) with x1!=x2 which contradicts as fog is one one so g should be one one

Related questions

0 votes
0 votes
0 answers
1
`JEET asked Jan 16, 2019
401 views
Let f(x, y) = (2x-y, x-2y), $\forall$(x, y) belongs $RxR$. Which of the following is true?f is one-to-one but not ontof is on-to but not one-to-one f is a bijectionf is n...
0 votes
0 votes
0 answers
2
0 votes
0 votes
0 answers
3
`JEET asked Dec 24, 2018
278 views
Which of the following is a bijection on set of all real numbers.$(1)f(x) = x{^2} $$(2)g(x) = |x|$$(3)h(x) = \left \lfloor x \right \rfloor$$(4)\phi(x)$ = $x^3$How to pro...
0 votes
0 votes
0 answers
4
!KARAN asked Dec 7, 2018
276 views
What is multi valued function. Find the number of multi valued functions from set A to another set B, given that the cardinalities of the sets A and B are m and n respect...