SOLUTION: The function $f$ satisfies \[f(\sqrt{x + 1}) = \frac{1}{x}\]for all $x \ge -1,$ $x\neq 0.$ Find $f(2)$.

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Question 1088254: The function $f$ satisfies
\[f(\sqrt{x + 1}) = \frac{1}{x}\]for all $x \ge -1,$ $x\neq 0.$ Find $f(2)$.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We have f%28sqrt%28x%2B1%29%29 and we want to find f%282%29. The inner terms sqrt%28x%2B1%29 and 2 must be equal. So we have

sqrt%28x%2B1%29+=+2

which solves to

sqrt%28x%2B1%29+=+2
%28sqrt%28x%2B1%29%29%5E2+=+2%5E2
x%2B1+=+4
x%2B1-1+=+4-1
x+=+3

Now let's plug x = 3 into the function below

f%28sqrt%28x%2B1%29%29+=+1%2Fx
f%28sqrt%283%2B1%29%29+=+1%2F3
f%28sqrt%284%29%29+=+1%2F3
f%282%29+=+1%2F3