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

 Oct 26, 2019
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\(f(2)=f(\sqrt{x+1})\)

 

solve for x

 

\(2=\sqrt{x+1}\)

\(2^2=\sqrt{x+1}^2\)

\(4=x+1\)

\(3=x\)

 

now plug \(x=3\) into \(f(\sqrt{x+1})\)

 

\(f(2)=f(\sqrt{x+1})=1/x\)

\(f(2)=f(\sqrt{3+1})=1/3\)

 

Therefore, f(2) = 1/3

 Oct 27, 2019

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