what comes in my mind is Wolfram|Alpha: Computational Knowledge Engine , but the result you would get depend on how you will enter the data,
Can you advise of a website or free software application where I can access a scientific calculator the capability to solve a function such as
f(x) = (x^2 -1) / (ln x + x+1 )
where I can enter the function and then enter any variable for x, without having to re-enter the function each time.
I also wish the calculator to be able to create a table of x and f(x) values around a specified x value or limit, and create a graph of the function.
Sounds like microsoft excel would do the job. You don't need anything fancy except for finding the solution to the equation, you could make a simple calculator using Newton's method and use finite differences if you dont want to get the derivative yourself for each function.
There are several free programs that fit your requirements. Here's one used by a lot of people:
Graph | Plotting of mathematical functions
As with any software, there is the problem of learning to use it. I think Graph is one of the easiest to learn.
Thanks to everyone who has offered a suggestion so far. I will reply herein to each.