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Draw the graph of the function f(x) = x-...

Draw the graph of the function `f(x) = x-|x2-x| -1 le x le 1`, where `[*]` denotes the greatest integer function. Find the points of discontinuity and non-differentiability.

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To solve the problem of drawing the graph of the function \( f(x) = x - |x^2 - x| \) for \( -1 \leq x \leq 1 \) and finding points of discontinuity and non-differentiability, we can follow these steps: ### Step 1: Understand the function The function involves an absolute value, so we need to analyze the expression \( |x^2 - x| \). This expression can be rewritten based on the sign of \( x^2 - x \). ### Step 2: Determine the critical points Set the expression inside the absolute value to zero: \[ ...
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Knowledge Check

  • The domain of the function f(x)=(1)/(sqrt((x)-[x])) where [*] denotes the greatest integer function is

    A
    R
    B
    `R^(+)`
    C
    `R^(-)`
    D
    `R-Z`

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