Question

Encontre os valores de x para os quais está definida a função
f(x)= raiz de (x-1) (-x+4)

Answer 1

$f(x)=\sqrt{(x-1)(-x+4)}\\f(x)=0\\0=\sqrt{(x-1)(-x+4)}\\0=\sqrt{-x^2+4x+x-4}\\0=\sqrt{-x^2+5x-4}\\(0)^2=(\sqrt{-x^2+5x-4})^2\\0=-x^2+5x-4\\\Delta=b^2-4ac\\\Delta=(5)^2-4.(-1)(-4)=25-16=9\\x=\frac{-b\pm\sqrt{\Delta}}{2a}\\x=\frac{-5\pm\sqrt{9}}{-2}\\x=\frac{-5\pm3}{-2}\\x'=\frac{-5+3}{-2}=\frac{-2}{-2}=\boxed{1}\\x''=\frac{-5-3}{-2}=\frac{-8}{-2}=\boxed{4}$