f(x)=x raise to 2( x square)-3x+1,find k if f(2k)=2f(k) and f(2k)=f(k).

Asked by pooja dev | 20th Nov, 2010, 12:00: AM

Expert Answer:

Dear Student,

f (x) = x2 -3x +1

=> f (2k) = (2k)2 - 3(2k) + 1

=> f (2k) = 4k2 - 6k + 1

And f (k) = k2 -3k +1

As, f (2k) = 2f (k)

=> 4k2 - 6k + 1 = 2k2 -6k +2

=> 2k2 -1 = 0

=> k2 = 1/2

=> k = 1/√2 or -1/√2

And for f (2k) = f (k)

i.e. 4k2 - 6k + 1 = k2 -3k +1

=> 3k2 - 3k = 0

=> 3k (k-1) = 0

=> k = 0 or 1.

Regards Topperlearning.

 

Answered by  | 21st Nov, 2010, 12:14: PM

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