Question

Seja a funçao f(x) = 3x²-bx + c , em que f(2) = 10 e f(-1) =3 . Calcule b , c e o valor da expressao f(3) + 2.f(1

Answer 1

Resposta:

$f(x)=3x^{2}-bx+c\\f(2)=10=>3*(2)^{2}-(b*2)+c=10\\12-2b+c=10\\12-10=2b-c\\2=2b-c\\2b-c=2\\\\f(-1)=3=>3*(-1)^{2}-b*(-1)+c=3\\3+b+c=3\\b+c=3-3\\b+c=0\\\\Logo;\\|b=-c|\\Substitui;\\|2b-c=2|\\2*(-c)-c=2\\-2c-c=2\\|-3c=2|*(-1)\\3c=-2\\\boxed {c=-\frac{2}{3}}\\b+c=0\\b-\frac{2}{3}=0\\\boxed {b=\frac{2}{3}}\\\\f(x)=3x^{2}-\frac{2}{3}x-\frac{2}{3}\\f(3)=3*(3)^{2}-(\frac{2}{3}*3)-\frac{2}{3}\\f(3)=27-2-\frac{2}{3}\\f(3)=25-\frac{2}{3}$

$f(1)=3x^{2}-bx+c\\f(1)=3*1-(\frac{2}{3}*1)-\frac{2}{3}\\f(1)=3-\frac{2}{3}-\frac{2}{3}\\f(1)=3-\frac{4}{3}\\\\Logo;\\f(3)+2*f(1)\\|25-\frac{2}{3}|+2*|3-\frac{4}{3}|$

$25+6-\frac{2}{3}-\frac{8}{3}\\\frac{(3*25)+(3*6)-2-8}{3}\\\frac{75+18-2-8}{3}\\\frac{93-10}{3}=\boxed {\frac{83}{3}}\\\\f(3)+2f(1)=\boxed {\frac{83}{3}}$

Explicação passo-a-passo: