Onto what?
What is the domain?
What is the image set?
I need to prove is an onto function. I'm kind of hazy here, am I supposed to subsitute and solve for x? Such as, . IF that is the case, I can't get it to add up to prove that function is onto. I know answer to problem, its just I think I'm jackng up my algebra and want to be able to do all the steps involved.
Thanks!
Here's what you do:
Suppose f is onto. Then there exists an x such that f(x) = (x+1)/(x) = y. Solve for x to get x = 1/(y-1). Now plug this value back into the equation, like this:
f(1/(y-1)) = (x+1)/(x) = [(1/(y-1))+1]/[1/(y-1)]. Now solve this equation to end up with f(1/(y-1)) = y. There, now you have proved that f(x) is onto.
That is what I was orignally doing. I know the problem is I'm messing up my algebra. I can't solve for x, I always end up cancelling my x-variables. Sorry, my algebra is rusty.
y=((x+1)/x) ...multiply both sides by x
xy=x+1 ...subtract 1
xy-1=x ...divide by (y-1)
x=x/(y-1)
Stuck here, not even sure if I did those steps properly.