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

 Jul 16, 2021
 #1
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we are given $f(\sqrt{x + 1}) = \frac{1}{x}$, but we know that $\sqrt{x + 1} \equiv 2$ which gives you $x+1=4 \ \ \  \therefore \ \ \  x=3 $

 

knowing that we can put that x on the other hand and for the first side we can either plug in $3$ for x, or just use $f(2)$ for the whole thing (which ill be using as its... easier.):


so you get:


$\boxed{ f(2)=\frac{1}{3}}  $

 Jul 16, 2021

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