Recent questions tagged continuity

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Let $ g(x)= \begin{cases} -x & \ x \leq 1 \\ x+1 & \ x \geq 1 \end{cases}$ and $ f(x)= \begin{cases} 1-x & \ x \leq 0 \\ x^{2} & \ x 0 \end{cases}$.Consider the co...
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If a continuous function $f(x)$ does not have a root in the interval $[a, b]$, then which one of the following statements is TRUE?$f(a) . f(b)=0$$f(a) . f(b) < 0$$f(a) . ...
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