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a) đkxđ: \(\left\{{}\begin{matrix}2x+1\ge0\\x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{-1}{2}\\x\ne0\end{matrix}\right.\)
b) đkxđ: \(2x^2+1\ge0\) (luôn thỏa mãn \(\forall x\in R\) )
c) đkxđ: \(\left\{{}\begin{matrix}x-1>0\\x+3>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>1\\x>-3\end{matrix}\right.\) \(\Leftrightarrow x>1\)
d) đkxđ: \(\left\{{}\begin{matrix}x^2-4\ne0\\x+1\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\pm2\\x\ge-1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne2\\x\ge-1\end{matrix}\right.\)
Lời giải:
a.
\(\left\{\begin{matrix} x\neq 0\\ 2x-1\geq 0\\ x^2-3x+2=(x-1)(x-2)\neq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\neq 0\\ x\geq \frac{1}{2}\\ x\neq 1; x\neq 2\end{matrix}\right.\)
$\Leftrightarrow x\geq \frac{1}{2}; x\neq 1; x\neq 2$
b. \(\left\{\begin{matrix}
x^2-1=(x-1)(x+1)\neq 0\\
7-2x\geq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix}
x\neq \pm 1\\
x\leq \frac{7}{2}\end{matrix}\right.\)
c.
\(\left\{\begin{matrix} x\neq 0\\ 4-2x+x^2\neq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\neq 0\\ (x-1)^2+3\neq 0\end{matrix}\right.\Leftrightarrow x\neq 0\)
d.
\(\left\{\begin{matrix} 25-x^2=(5-x)(5+x)\geq 0\\ x\geq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} -5\leq x\leq 5\\ x\geq 0\end{matrix}\right.\Leftrightarrow 0\leq x\leq 5\)
a) \(y=\dfrac{1}{x}-\dfrac{\sqrt[]{2x-1}}{x^2-3x+2}\)
Điều kiện \(\) \(2x-1\ge0;x\ne0;x^2-3x+2\ne0\)
\(\Leftrightarrow x\ge\dfrac{1}{2};x\ne0;\left(x-1\right)\left(x-2\right)\ne0\)
\(\Leftrightarrow x\ge\dfrac{1}{2};x\ne0;x\ne1;x\ne2\)
ĐKXĐ: \(\left\{{}\begin{matrix}x-2>=0\\4-x>=0\\x+1< >0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2< =x< =4\\x< >-1\end{matrix}\right.\Leftrightarrow x\in\left[2;4\right]\)
a)
Đkxđ: \(\left\{{}\begin{matrix}-3x+2\ge0\\x+1\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\le\dfrac{-2}{3}\\x\ne-1\end{matrix}\right.\)
b)
Đkxđ: \(\left\{{}\begin{matrix}x-2\ge0\\-x-4\ge0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge2\\x\le4\end{matrix}\right.\)\(\Leftrightarrow2\le x\le4\).
c)
Đkxđ: \(\left\{{}\begin{matrix}3x^2+6x+11>0\\2x+1\ge0\end{matrix}\right.\)\(\Leftrightarrow2x+1\ge0\)\(\Leftrightarrow x\ge-\dfrac{1}{2}\).
d)
Đkxđ: \(\left\{{}\begin{matrix}x+4\ge0\\x^2-9\ne0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-4\\x\ne3\\x\ne-3\end{matrix}\right.\).
a) đk \(\left\{{}\begin{matrix}2x+1\ge0\\x\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{1}{2}\\x\ne0\end{matrix}\right.\)
b) đk \(x+3>0\Leftrightarrow x>-3\)
c) \(\left\{{}\begin{matrix}x-1>0\\x\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x>1\\x\ge0\end{matrix}\right.\Leftrightarrow x>1\)
d) đk \(\left\{{}\begin{matrix}x^2-4\ne0\\x+1\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\x\ne\pm2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\x\ne2\end{matrix}\right.\)
1) \(\sqrt[]{3x+7}-5< 0\)
\(\Leftrightarrow\sqrt[]{3x+7}< 5\)
\(\Leftrightarrow3x+7\ge0\cap3x+7< 25\)
\(\Leftrightarrow x\ge-\dfrac{7}{3}\cap x< 6\)
\(\Leftrightarrow-\dfrac{7}{3}\le x< 6\)
a) Đkxđ: \(x-5\ne0\Leftrightarrow x\ne5\).
b) Đkxđ: \(x\in R\).
c) Đkxđ: \(x^2-x-2\ge0\)\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\ge0\)
Th1: \(\left\{{}\begin{matrix}x-1\ge0\\x-2\ge0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x\ge2\end{matrix}\right.\)\(\Leftrightarrow x\ge2\).
Th2: \(\left\{{}\begin{matrix}x-1< 0\\x-2< 0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x< 1\\x< 2\end{matrix}\right.\)\(\Leftrightarrow x< 1\).
Đkxđ: \(\left[{}\begin{matrix}x\ge2\\x< 1\end{matrix}\right.\).
d) Đkxđ: \(x\in R\).