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

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) (Show Source): You can put this solution on YOUR website!
We have and we want to find . The inner terms and must be equal. So we have

which solves to

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

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