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

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


   

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(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.

You are given


    f%28sqrt%28x%2B1%29%29 = 1%2Fx.    (1)


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


In other words, you want to have


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


It implies  (after squaring both sides) 

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


Indeed,  then  sqrt%283%2B1%29 = sqrt%284%29 = 2.


Very good.   Then at x= 3,  the right side of the equation (1) is  1%2Fx = 1%2F3.


ANSWER.  f(2) = 1%2F3.

Solved.

Is everything clear to you in my solution ?


`````````````````````````````````

If after reading my post you will have questions,  do not hesitate to post them to me.

If you do,  then please refer to the  ID  number of this problem,  which is  1164402.

The  ID  number is the first number,  which you see in your page in the  UPPER  LEFT  corner.

If you will post to me without referring to this  ID  number,  I will not know to whom to answer.

It is how this forum works.

So,  mentioning this ID is  NECESSARY,  if you want to have two-way communication with me.