# Find Exact Value of fg(4): Learn Terminology

• thomas49th

#### 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

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?

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.

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 :)

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).

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!