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Another function problem (Posted on 2006-11-19) Difficulty: 3 of 5
Define a sequence of functions f0, f1, f2, ......, by

f0(x)= 8, for all real x, and
fn+1(x) = sqrt(x2 + 6fn(x)); for all real x and all non-negative integers n.

Solve the equation

fn(x)= 2x

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(7): Solution? | Comment 8 of 12 |
(In reply to re(6): Solution? by tomarken)

x=-4 does not work, in my opinion, because sqrt is normally taken to be nonnegative which means that f_n(x) cannot equal -8. Squaring both sides of f_n(x)=2x has caused an extraneous solution to appear, I believe.

  Posted by Richard on 2006-11-19 20:40:39

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