Question

Ajudaa

3. Dada a função g(x) = -x² + 5x + 3, calcule:

a) g (√2)

b) g (2/3)

Answer 1

$\mathsf{g(x)=-x^2+5x+3}$

a)

$\mathsf{g(\sqrt{2})=-(\sqrt{2})^2+5\cdot\sqrt{2}+3}\\\\ \mathsf{g(\sqrt{2})=-(\sqrt{2}\cdot\sqrt{2})+5\sqrt{2}+3}\\\\ \mathsf{g(\sqrt{2})=-(\sqrt{4})+5\sqrt{2}+3}\\\\ \mathsf{g(\sqrt{2})=-2+5\sqrt{2}+3}\\\\ \boxed{\mathsf{g(\sqrt{2})=1+5\sqrt{2}}}$


b)

$\mathsf{g\left(\dfrac{2}{3}\right)=-\left(\dfrac{2}{3}\right)^2+5\cdot\dfrac{2}{3}+3}\\\\\\ \mathsf{g\left(\dfrac{2}{3}\right)=-\left(\dfrac{2}{3}\cdot\dfrac{2}{3}\right)+\dfrac{10}{3}+3}\\\\\\ \mathsf{g\left(\dfrac{2}{3}\right)=-\dfrac{4}{9}+\dfrac{10+9}{3}}\\\\\\ \mathsf{g\left(\dfrac{2}{3}\right)=-\dfrac{4}{9}+\dfrac{19}{3}}\\\\\\ \mathsf{g\left(\dfrac{2}{3}\right)=-\dfrac{4}{9}+\dfrac{57}{9}}\\\\\\ \boxed{g\left(\mathsf{\dfrac{2}{3}\right)=\dfrac{53}{9}}}$