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最新文章数学笔记01：函数与极限
函数
函数定义域
①分母不为零 \[1\over f(x)\] \[f(x)\neq0\]
②偶次根式 \[\sqrt[2n]{f(x)}\]
\[f(x)\geq0\]
③对数函数 \[lnf(x)\] \[f(x)>0\]
④反三角函数 \[arcsin f(x)\] \[ arccosf(x) \] \[ -1\leq f(x)\leq 1\]
例1：求函数\[y=ln{x \over
x-2}+arcsin{3x-1\over5}\]的定义域
解： \[
\left\{
\begin{array}{c}
{x\over x-2}>0\\
-1\leq{3x-1\over5}\leq 1\\
\end{array}
\right.\\
\Rightarrow -{4\over3}\leq x \leq 0
\]
例2：\[f(2x+3)=x^2\]，求\[f(x)\]
解： \[
令t=2x+3 \Rightarrow x={t-3\over2}\\
得f( ...
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