SOLUTION: The function f satisfies f(sqrt(x+1))=1/x For all x >= -1, x does not equal 0. Find f(2).

Question 1164402: The function f satisfies
f(sqrt(x+1))=1/x
For all x >= -1, x does not equal 0. Find f(2).
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
.


You are given


     = .    (1)


You want to make the argument of the function f equal to 2.


In other words, you want to have


     = 2.


It implies  (after squaring both sides) 

    x + 1 = 4,  and then  x = 4-1 = 3.


Indeed,  then   =  = 2.


Very good.   Then at x= 3,  the right side of the equation (1) is   = .


ANSWER.  f(2) = .

Solved.

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