• Support PF! Buy your school textbooks, materials and every day products Here!

Find the compositions of these functions?

  • #1
438
0
Given two functions , f(x)=x^2+3 , where x is real , g(x)=|x|-5 , x is real , find gf(x).

i found gf(x)=x^2-2

is it true that the range of gf(x) is the same as the range of g(x) ? If so,

the range of g(x) is [-5 , infinity) and the range of gf(x) is [-2 , infinity)

why arent they the same ?
 

Answers and Replies

  • #2
28
0


I think everything is correct, why would you think the range of g(f(x)) is the same as the range of g(x)?
 
  • #3
954
117


I'll pose the reverse question: why should they be the same? g(x) and gf(x) are different functions.
 
  • #4
438
0


Take a look at the diagram i attached . Isn't that the image of gf(x) the same as the image function g(x) ?
 
  • #5


The range of [itex]f[/itex] needn't be the whole of the domain of [itex]g[/itex] so some of the images under [itex]g[/itex] may not occur in [itex]gf[/itex]. You only have [itex]range(gf)\subseteq range(g)[/itex]. In fact you could say they're not equal because you have yourself provided a counterexample.
 
  • #6
438
0


The range of [itex]f[/itex] needn't be the whole of the domain of [itex]g[/itex] so some of the images under [itex]g[/itex] may not occur in [itex]gf[/itex]. You only have [itex]range(gf)\subseteq range(g)[/itex]. In fact you could say they're not equal because you have yourself provided a counterexample.
thanks Martin , how about the domains , is the domain of f(x) the same as domain gf(x) because both of them started from the same set or it needn't also be the same in this case.
 
  • #7


Yes, [itex]dom(gf)=dom(f)[/itex], assuming you only define the composition [itex]gf[/itex] when [itex]range(f)\subseteq dom(g)[/itex].
 
  • #8
438
0


Yes, [itex]dom(gf)=dom(f)[/itex], assuming you only define the composition [itex]gf[/itex] when [itex]range(f)\subseteq dom(g)[/itex].
thanks again Martin !
 

Related Threads for: Find the compositions of these functions?

Replies
3
Views
1K
Replies
9
Views
2K
Replies
2
Views
3K
  • Last Post
Replies
3
Views
411
Replies
10
Views
2K
Replies
6
Views
774
  • Last Post
Replies
3
Views
380
  • Last Post
Replies
8
Views
2K
Top