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Examine the continuity of f(x) ={(1-x,x ...

Examine the continuity of f(x) =`{(1-x,x lt1),(0,x=1),(1+x,x gt1):}`

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To examine the continuity of the function \( f(x) \) defined as: \[ f(x) = \begin{cases} 1 - x & \text{if } x < 1 \\ 0 & \text{if } x = 1 \\ 1 + x & \text{if } x > 1 ...
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Knowledge Check

  • f(x) = {((2x+1), x lt 1),(2,x=1),(x^(2)+1, x gt 1):} is

    A
    continuous at x = 1
    B
    left continuous at x = 1
    C
    right continuous at x = 1
    D
    none of these

  • If f(x) = {{:(e^(x), x lt=0),(|1-x| ,x gt 0):} then

    A
    f(x ) is differentiable at x = 0
    B
    f (x ) is continuous at x = 0,1
    C
    f (x ) is differentiable at x = 1
    D
    None of the above

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