Question

Considere a função:

$f(x)= \frac{ x^{2} -5x+6}{x-2}$

Qual é o valor de $f (\frac{1}{2})$ ?

Answer 1

$f(x)=\dfrac{x^2-5x+6}{x-2}$


O valor de $f\left(\dfrac{1}{2}\right)$ é obtido fazendo $x=\dfrac{1}{2}$ na expressão acima:

$f\left(\dfrac{1}{2}\right)=\dfrac{\left(\frac{1}{2} \right )^2-5\cdot \frac{1}{2}+6}{\frac{1}{2}-2}\\\\\\ =\dfrac{\frac{1}{4}-\frac{5}{2}+6}{\frac{1}{2}-2}\\\\\\ =\dfrac{\frac{1}{4}-\frac{5}{2}+6}{\frac{1}{2}-2}\cdot \dfrac{4}{4}\\\\\\ =\dfrac{\left(\frac{1}{4}-\frac{5}{2}+6 \right )\cdot 4}{\left(\frac{1}{2}-2 \right )\cdot 4}$

$=\dfrac{1-10+24}{2-8}\\\\\\ =\dfrac{15}{-6}\\\\\\ =-\,\dfrac{15}{6}\begin{array}{c}^{\div 3}\\^{\div 3} \end{array}\\\\\\ =-\,\dfrac{5}{2}\\\\\\\\ \therefore~~\boxed{\begin{array}{c} f\left(\dfrac{1}{2}\right)=-\,\dfrac{5}{2} \end{array}}$


Bons estudos! :-)