定义域 f(x)=sqrt((2x+1)/(x^2-1))

解答

定义域

f (x) = \frac{2 x + 1}{x ^{2} - 1}

- 1 < x \leq - \frac{1}{2} or x > 1

间隔符号

(- 1, - \frac{1}{2}] \cup (1, \infty)

求解步骤

对于根式找到非负值:

- 1 < x \leq - \frac{1}{2} or x > 1

找到无定义的点（奇点）:

x = 1, x = - 1

合并考虑函数有实数值的区域与未定义的点得出最终的函数定义域

- 1 < x \leq - \frac{1}{2} or x > 1

d o main y = ln (x + 5)

d o main f (x) = \frac{2}{x - 8} + 9

d o main f (x) = \frac{1}{5 x + 1}

d o main f (x) = ln (x^{2} - 5)

d o main f (x) = 2 sin (2 x)