Find all points of discontinuity of f- where f isdefined by f x - - x - 1 if x - 0- x2 - 1 if x - 0 -

f( x ) =∫ x+1 x≥ 0 #160; x ^ 2 +1 x≤ 0 #160; #160; Let= sin x⟶ 0 f( x ) =1 LXC #10;= RXC = #160; f(0) ...

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Trigonometric Ratios of Allied Angles

Find all poin...

Question

Find all points of discontinuity of $f$ , where $f$ is
defined by $f (x) = {\begin{matrix} x + 1 i f x \geq 0 x^{2} + 1 i f x \leq 0 \end{matrix}$

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f

f

⎧ ⎨ ⎩ \begin{matrix} \frac{x}{| x |} if x < 0 - 1 if x \geq 0 \end{matrix}

f (x),

f (x) = {\begin{matrix} x + 1 i f x \geq 1 x^{2} + 1 i f x < 1 \end{matrix}}

Find all points of discontinuity of f, where f is defined by

lim x \to 0 f (x)

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} x - 1 & i f & x < 0 0 & i f & x = 0 x + 1 & i f & x > 0 \end{matrix}

f

f

f (x) =

⎧ ⎨ ⎩ \begin{matrix} \frac{| x |}{x}, if x \neq 0 0, if x = 0 \end{matrix}

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