Find Exact Value of fg(4): Learn Terminology

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In summary, the conversation discusses the terminology of functions and clarifies the meaning of fg(4) as either the product of two functions or the composition of two functions. The conversation also mentions the use of inverse functions and how they are written using a negative exponent.
  • #1
thomas49th
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It's just the terminology but I am 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 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
 
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  • #3
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
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
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
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
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!
 

1. What does "fg(4)" mean in this context?

"fg(4)" represents the function fg evaluated at the input value of 4. In other words, it is asking for the value of the function fg when the input is 4.

2. What does "exact value" mean?

"Exact value" refers to the precise numerical result of a calculation or measurement, as opposed to an approximation or estimation.

3. What is a function?

A function is a mathematical relationship between an input (often called the independent variable) and an output (often called the dependent variable). It assigns a unique output to each input, and can be represented graphically, algebraically, or verbally.

4. What does "terminology" refer to in this context?

In this context, "terminology" refers to the specific vocabulary and terminology used in mathematics to describe and discuss concepts, operations, and relationships.

5. Why is it important to find the exact value of a function?

Finding the exact value of a function allows for more precise and accurate calculations and predictions. It also helps to understand the behavior and properties of the function, and can be used to solve more complex problems and equations.

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