Thread: Composite Functions

Hello, just discovered this site and it looks to be very helpful! I have two questions regarding my Pre-Calc homework:

1. First Question:A function f is given which satisfies f(1/(x+1))= 2x-12 for all real numbers x. Compute f(1) and f(f(2)). What are the range and domain of f?

My understanding is that I can treat (1/(x+1)) like a g(x) and so for f(1), I would insert 1 and come up with f(1/2). Then I would plug in 1/2 into 2x+12 to get 1+12=13, so f(1)=13. Am I following these steps properly? Then for f(f(2)), would I insert a 2 into the input, calculate the output and then use that output as the next input to the same equation?

2. Second Question: Does there exist a function f which satisfies f(x^2)=x+1 for all real numbers x? I believe this function would just be f(x)=x^2+1 which I get by substituting x^2 into the output, but want to make sure there isn't something I am missing.

Any help would be greatly appreciated.

Originally Posted by leolson3

Hello, just discovered this site and it looks to be very helpful! I have two questions regarding my Pre-Calc homework:
1. First Question:[I]A function f is given which satisfies f(1/(x+1))= 2x-12 for all real numbers x. Compute f(1) and f(f(2)). What are the range and domain of f?

Look at it this way: if then

Once you have that, what is

Just realized I had a typo, above, it should indeed be 2x-12 as I initially put.

So a would equal 0 and f(1) would be -12?