5.1 根式&无理式 Radical & Irrational Expression - 练习题 - 独中课程 | 线上补习

(1)
Find the domain of x $\epsilon$ R such that the following statements are meaningful
在x $\epsilon$ R，求使下列各式有意义的定义域。

(a) $\sqrt{1-x}$

(b) $\sqrt[3]{2x-1}$

(c) $\sqrt[4]{2x-1}$

(d) $\sqrt{x^2+1}$

(e) $\sqrt{x^2-1}$

(f) $\sqrt[5]{1-x^2}$

(a)

*** QuickLaTeX cannot compile formula:
\xle1

*** Error message:
Undefined control sequence \xle.
leading text: $\xle

(b) $x \epsilon R$
(c) $x\geq\frac{1}{2}$
(d) $x \epsilon R$
(e)

*** QuickLaTeX cannot compile formula:
\xle-1, x\geq1

*** Error message:
Undefined control sequence \xle.
leading text: $\xle

(f) $x \epsilon R$

(2)
Calculate 计算

(a) $\left(\sqrt[7]{2-x}\right)^7$

(b) $\sqrt[4]{81{(1+2x)}^4}$

(c) $\sqrt{25x^2-10x+1} \left(x>{\frac{1}{5} }\right)$ | Hint配方法

(d) $\sqrt{25x^2-10x+1} \left(x<{\frac{1}{5} }\right)$

(e) $\sqrt[4]{\left(3p-2\right)^4}-\sqrt{\left(p+2\right)^2} \left(-2<p<\frac{2}{3}\right)$

(a) $2-x$
(b) $3\left|1+2x\right|$
(c) $5x - 1$
(d) $1 - 5x$
(e) $-4p$