Cook Harmon
05/10/2024 · Senior High School
Consider the \( \mathbb{R}^{2}-\mathbb{R} \) function \( f \) defined by \[ f(x, y)=\left\{\begin{array}{cll}\frac{x^{2}-2 x y+3 x}{x} & \text { if } & x \neq 0 \\ 2 & \text { if } \quad(x, y)=(0,0)\end{array}\right. \] (a) Write down the largest possible domain \( D_{f} \) of \( f \).
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The largest possible domain \( D_f \) of the function \( f \) is \( \mathbb{R}^2 \) excluding the vertical line \( x = 0 \) for \( y \neq 0 \) and including the point \( (0, 0) \).
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