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f-2-x-2f-x-x-2-8x-15-f-x-

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Question Number 195391 by mathlove last updated on 01/Aug/23
f^2 (x)+2f(x)=x^2 −8x+15 f(x)=?
f2(x)+2f(x)=x2−8x+15f(x)=?
Answered by MM42 last updated on 01/Aug/23
(f+1)^2 =x^2 −8x+16=(x−4)^2 ⇒f=∣x−4∣−1 ✓
(f+1)2=x2−8x+16=(x−4)2⇒f=∣x−4∣−1✓
Answered by kapoorshah last updated on 01/Aug/23
let f(x) = ax + b (ax + b)^2 + 2(ax + b) = x^2 − 8x +15 a^2 x^2 + 2abx + b^2 + 2ax + 2b = x^2 − 8x +15 a^2 x^2 + (2ab + 2a)x + b^2 + 2b = x^2 − 8x +15 a^2 = 1 a = 1 a = −1 2b + 2 = −8 −2b − 2 = −8 b = −5 b = 3 ∴ f(x) = x − 5 ∴ f(x) = −x + 3
letf(x)=ax+b(ax+b)2+2(ax+b)=x2−8x+15a2x2+2abx+b2+2ax+2b=x2−8x+15a2x2+(2ab+2a)x+b2+2b=x2−8x+15a2=1a=1a=−12b+2=−8−2b−2=−8b=−5b=3∴f(x)=x−5∴f(x)=−x+3

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