Menu Close

f-x-x-3-3x-2-1-1-calcul-h-X-f-a-X-b-2-determine-a-and-b-such-that-h-is-odd-

Tinku Tara 0 Comments
Pin




Question Number 193542 by SAMIRA last updated on 16/Jun/23
f(x) = x^3 +3x^2 −1 1) calcul h(X) = f(a+X) −b 2) determine a and b such that h is odd
f(x)=x3+3x2−11)calculh(X)=f(a+X)−b2) determine a and b such that h is odd
Commented by a.lgnaoui last updated on 17/Jun/23
odd?
odd?
Commented by SAMIRA last updated on 17/Jun/23
uneven
uneven
Answered by mr W last updated on 17/Jun/23
2) h(x)=−h(−x) f(x+a)−b=−f(−x+a)+b f(x+a)=−f(−x+a)+2b (x+a)^3 +3(x+a)^2 −1=−(−x+a)^3 −3(−x+a)^2 +1+2b (x+a)^3 +(−x+a)^3 +3(x+a)^2 +3(−x+a)^2 =2+2b 3(a+1)x^2 +a^3 +3a^2 =1+b ⇒a+1=0 ⇒a=−1 ⇒1+b=a^3 +3a^2 ⇒b=1
2)h(x)=−h(−x)f(x+a)−b=−f(−x+a)+bf(x+a)=−f(−x+a)+2b(x+a)3+3(x+a)2−1=−(−x+a)3−3(−x+a)2+1+2b(x+a)3+(−x+a)3+3(x+a)2+3(−x+a)2=2+2b3(a+1)x2+a3+3a2=1+b⇒a+1=0⇒a=−1⇒1+b=a3+3a2⇒b=1

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *