If f(x) = 2x and g(x) = x^$\frac{2}{2}$ + 1, then which of the following can be a discontinuous function ______.

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If f(x) = 2x and g(x) = x^$\frac{2}{2}$ + 1, then which of the following can be a discontinuous function ("g"(x))/("f"(x)). Explanation: We know that the algebraic polynomials are continuous functions everywhere. $\therefore$ f(x) + g(x) is continuous .....`[(∵ "Sum, difference and product"),("of two continuous functions is"),("also continuous")]` f(x) – g(x) is continuous f(x) . g(x) is continuous ("g"(x))/("f"(x)) is only continuous if g(x) $\neq$ 0 $\therefore$ `("f"(x))/("g"(x)) = (2x)/(x^$\frac{2}{2}$ + 1) = (4x)/(x^2 + 2) Here, ("g"(x))/("f"(x)) = (x^$\frac{2}{2}$ + 1)/(2x) = (x^2 + 2)/(4x)` Which is discontinuous at x = 0.

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