Question

найдите область определения функции:
y = $sqrt[6]{3-x}$ + $frac{sin x }{ sqrt[4]{5x-1} } - sqrt{5 x^{2} -16x + 3 }$

Answer 1

$y = sqrt[6]{3-x} + frac{sin x }{ sqrt[4]{5x-1} } - sqrt{5 x^{2} -16x + 3 }$

$3-x geq 0 \ x leq 3 \\ 5x-1>0 \ x>0.2 \\ 5 x^{2} -16x + 3 geq 0 \ 5 x^{2} -16x + 3 =0 \ D_1=64-15=49 \ x_1=1.2 \ x_2=0.2 \ x leq 0.2; x geq 1.2$

$x leq 3 \ x>0.2 \ x leq 0.2; x geq 1.2 \\ 1.2 leq x leq 3$