定义域 f(x)=sqrt((100-x^2)/(x^2+4x-21))

解答

定义域

f (x) = \frac{100 - x ^{2}}{x ^{2} + 4 x - 21}

- 10 \leq x < - 7 or 3 < x \leq 10

间隔符号

[- 10, - 7) \cup (3, 10]

求解步骤

对于根式找到非负值:

- 10 \leq x < - 7 or 3 < x \leq 10

找到无定义的点（奇点）:

x = 3, x = - 7

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

- 10 \leq x < - 7 or 3 < x \leq 10

d o main f (x) = \frac{x ^{2} + 2 x - 3}{2 x ^{2} - 4 x}

d o main f (x) = \frac{x + 1}{x ^{2}}

d o main cos (2 x)

d o main f (x) = x^{2} - 4 x - 5

d o main \frac{x ^{2}}{x ^{2} - 1}