Question

[Phan Trân Mẫn]

Tìm tập xác định của các hàm số sau đây :
a) y= \(\sqrt{x-2}\)
b) y= \(\sqrt{4x-3}\)
c) y= \(\frac{2x-1}{\sqrt{x+2}}\)
d) y= x + \(\frac{1}{\sqrt{3-x}}\)
e) y= x² + 1 + \(\frac{1}{\sqrt{4-3x}}\)
f) y= \(\sqrt{x^2+2}\) + \(\sqrt{x}\)
g) y= \(\sqrt{x^2-2x+1}\) + \(\sqrt{2-3x}\)
h) y= \(\sqrt{2+x}\) + \(\sqrt{x-2}\)
i) y= \(\sqrt{2+x}\) + \(\sqrt{2-x}\)

Answer 1

[Akai Haruma]

a)

ĐK: $x-2\geq 0\Leftrightarrow x\geq 2$

TXĐ: $[2;+\infty)$

b)

ĐK: $4x-3\geq 0\Leftrightarrow x\geq \frac{3}{4}$

TXĐ: $[\frac{3}{4};+\infty)$

c) ĐK: \(x+2>0\Leftrightarrow x>-2\)

TXĐ: $(-2;+\infty)$

d)

ĐK: $3-x>0\Leftrightarrow x< 3$

TXĐ: $(-\infty; 3)$

e)

$4-3x>0\Leftrightarrow x< \frac{4}{3}$

TXĐ: $(-\infty; \frac{4}{3})$

Answer 2

[Akai Haruma]

f)

ĐK:\(\left\{\begin{matrix} x^2+2\geq 0\\ x\geq 0\end{matrix}\right.\Leftrightarrow x\geq 0\)

TXĐ: $[0;+\infty)$

g) ĐK: \(\left\{\begin{matrix} x^2-2x+1\geq 0\\ 2-3x\geq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} (x-1)^2\geq 0\\ x\leq\frac{2}{3}\end{matrix}\right.\Leftrightarrow x\leq \frac{2}{3}\)

TXĐ: $(-\infty; \frac{2}{3}]$

h)

ĐK: \(\left\{\begin{matrix} 2+x\geq 0\\ x-2\geq 0\end{matrix}\right.\Leftrightarrow x\geq 2\)

TXĐ: $[2;+\infty)$

i)

ĐK: \(\left\{\begin{matrix} 2+x\geq 0\\ 2-x\geq 0\end{matrix}\right.\Leftrightarrow 2\geq x\geq -2\)

TXĐ: $[-2;2]$