Find Exact Value of fg(4): Learn Terminology

[thomas49th]

It's just the terminology but I am just unsure what it means
I have 2 functions
f(x) = ln(2x-1)
g(x) = \frac{2}{x-3}

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

now what exactly 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

 

[thomas49th]

ermm well the question is 5 a and here is the mark scheme:

http://eiewebvip.edexcel.org.uk/Reports/Confidential Documents/0706/6665_01_rms_20070815.pdf

i've glanced through my textbook and i can't find it :S

 

[HallsofIvy]

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 f \circle g(x) 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?

 

[HallsofIvy]

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.

 

[thomas49th]

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 :)

 

[Osmean]

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).

 

[HallsofIvy]

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!