1
$g(x)=\sqrt{x+۱}\times \sqrt{x\,},\,f(x)=\sqrt{{{x}^{۲}}+x}$
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2
$g(x)=x-۱\,,\,f(x)=\frac{{{x}^{۲}}-۱}{x+۱}$
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3
$g(x)={{x}^{۲}}-۱\,,\,f(x)=\frac{{{x}^{۴}}-۱}{{{x}^{۲}}+۱}$
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4
$g(x)={{(\sqrt{x})}^{۲}}\,,\,f(x)=\sqrt{{{x}^{۲}}}$
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خطا
بررسی گزینهها: 1) ${{D}_{f}}:{{x}^{2}}+x\ge 0\Rightarrow x(x+1)\ge 0\Rightarrow x\le -1$ یا $x\ge 0$ ${{D}_{g}}:\left\{ \begin{matrix}x+1\ge 0\Rightarrow x\ge -1 \\x\ge 0 \\\end{matrix} \right.\Rightarrow x\ge 0\,\,\,\,\,\Rightarrow \,{{D}_{f}}\ne {{D}_{g}}\Rightarrow f\ne g$ 2) ${{D}_{f}}=\mathbb{R}-\left\{ -1 \right\}\,,\,{{D}_{g}}=\mathbb{R}\Rightarrow f\ne g$ 4) ${{D}_{f}}=\mathbb{R}\,,\,{{D}_{g}}=\left[ 0\,,\,+\infty \right]\Rightarrow f\ne g$