f(x) = x2 - 3x + 1, find k if f(2k) = 2f(k) and f(2k) = f(k) - Maths - Sets

Question

f(x) = x2 - 3x + 1, find k if
f(2k) = 2f(k) and f(2k) = f(k)

Sunanta Meitei · Accepted Answer

Hi Narayana!
Here is the answer to your question
f(x) = x2 – 3x +
1
f(2k) = 2f(k)
∴ (2k)2 – 3(2k) + 1 = 2
(k2 – 3k + 1)
⇒ 4k2 – 6k + 1 =
2k2 – 6k + 2
⇒ 2k2 – 1 = 0
<img height="90" width="200" src=
"https://s3mn%20mnimgs%20com/img/shared/userimages/mn_images/image/k(1)%20png"
alt="">
f(2k) = f(k)
∴ (2k)2 – 3(2k) + 1 =
k2 – 3k + 1
⇒ 4k2 – 6k + 1 =
k2 – 3k + 1
⇒ 3k2 – 3k = 0
⇒ 3k (k – 1) = 0
⇒ k = 0 or k – 1 = 0
⇒ k = 0 or k = 1
The value of k is 0 or 1
Cheers!