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

Fg(x) - terminology

  • Thread starter thomas49th
  • Start date
  • #1
655
0
It's just the terminology but im just unsure what it means
I have 2 functions
f(x) = ln(2x-1)
g(x) = [tex]\frac{2}{x-3}[/tex]

the question is find the exact value of fg(4)

now what exaclty does that mean. I'm guessing we sub x = 4 into it at some point. It is asking for me to mulitply f(x) by g(x)

im not sure. can someone help me please. thanks
 

Answers and Replies

  • #3
HallsofIvy
Science Advisor
Homework Helper
41,792
920
I'm also not sure. Normally "fg(x)" means "f(x)*g(x)". That is, to find fg(4) you substitute x= 4 into both equations, then multiply the values. That is probably what is meant.

But it is possible that what you really mean is [itex]f \circle g(x)[/itex] which means f(g(x)). That is, substitute x= 4 into g: g(4). Then, whatever number you get for g(4), substitute that into f: f(g(4)).

Surely your textbook was discussing one or the other of those?
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,792
920
Okay, it does mean "composition of functions": f(g(x)). First find g(4)= 2/(4-3)= 2/1= 2 and then find f(2). Strictly speaking, that should be written with a little "o" between the functions.
 
  • #5
655
0
ahh cheerz i understand now, but can you explain part b. I though ^-1 means 1 over the term

ie x^(-1) = 1/x

What is part b asking really

thanks :)
 
  • #6
1
0
No. f^(-1)(x) means the inverse function of f(x).
So if y=f(x)=ln(2x-1), then you should solve for x and replace x by y and y by x. Then you have the inverse of f(x).
 
  • #7
HallsofIvy
Science Advisor
Homework Helper
41,792
920
For a number, x, x-1 means 1/x. For a function, f, f-1 means the inverse function, f(f-1(x))= x, f-1(f(x))= x. It's an unfortunate conflict of symbols but too late to change it now!
 

Related Threads for: Fg(x) - terminology

  • Last Post
Replies
3
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
1K
Replies
1
Views
1K
Replies
10
Views
2K
  • Last Post
Replies
1
Views
827
Replies
18
Views
1K
Top