$8.67 y=\sqrt[6]{4^{\frac{x+1}{x}}-17 \cdot 2^{\frac{1}{x}}+4}$.
8.67 The function is defined if

$$
4^{\frac{x+1}{x}}-17 \cdot 2^{\frac{1}{x}}+4 \geq 0, \text { i.e. } 2^{2\left(1+\frac{1}{x}\right)}-17 \cdot 2^{\frac{1}{x}}+4 \geq 0
$$

Let $\quad 2^{\frac{1}{x}}=y>0 ; \quad$ then we get the inequality
$4 y^{2}-17 y+4 \geq 0$, from which $y \leq \frac{1}{4}$ or $y \geq 4$. Therefore:

$2^{\frac{1}{x}} \leq \frac{1}{4} \Rightarrow \frac{1}{x} \leq-2 \Rightarrow \frac{1+2 x}{x} \leq 0 \Rightarrow-0.5 \leq x<0 ;$

$2^{\frac{1}{x}} \geq 4 \Rightarrow \frac{1}{x} \geq 2 \Rightarrow \frac{1-2 x}{x} \geq 0 \Rightarrow 0<x \leq 0.5$.

Answer: $[-0.5 ; 0) \cup(0 ; 0.5]$.