perplexus.info :: Numbers : Another function problem

Another function problem (Posted on 2006-11-19)

Define a sequence of functions f₀, f₁, f₂, ......, by

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

Solve the equation

f_n(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.)

Solution

| Comment 11 of 12 |

fn(x)=SQRT(x²+6sqrt(x²+6.......(till n terms)

fn(x)=2x

2x=sqrt(x²+6(2x))

4x²=x²+12x

3x²-12x=0

x(x-4)=0

x=0 or x=4

but f(0)=8≠2x(i.e 2(0))

hence ,x=4

Posted by Rajesh on 2006-11-21 13:17:42

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