Find the domain and range of the function \(\frac{x^2-4}{x-2}\).

1.	Find the domain and range of the function \(\frac{x^2-4}{x-2}\).
Answer» . Let y = \(\frac{x^2-4}{x-2}\) ⇒ y = x + 2 when x ≠ 2 Now \(\frac{x^2-4}{x-2}\) is not defined only when x = 2, therefore Domain of y = \(\frac{x^2-4}{x-2}\) is R - {2}. But y = x + 2 will take up all real values, but y = 4, when x = 2, (not possible) ∴ Range of function is R – {4}.

Answer»

. Let y = \(\frac{x^2-4}{x-2}\)

⇒ y = x + 2 when x ≠ 2

Now \(\frac{x^2-4}{x-2}\) is not defined only when x = 2, therefore

Domain of y = \(\frac{x^2-4}{x-2}\) is R - {2}.

But y = x + 2 will take up all real values, but y = 4, when x = 2, (not possible)

∴ Range of function is R – {4}.

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