Question

The function f defined by `f(x) = {{:(x, "if"  x ≤ 1),(5, "if"  x > 1):}` discontinuous at x equal to

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Answer 1

2

Explanation:

At `x` = 0

`lim_(x -> 0) - f(x) = lim_(x -> 0) - x` = 0

`lim_(x -> 0) + f(x) = lim_(x -> 0) + x` = 0

`f(0)` = 0

∴ If is continuous at `x` = 0

At `x` = 1

`lim_(x -> 1) + f(x) = lim_(x -> 1) + (x)` = 1

`lim_(x -> 1) f(x) = lim_(x -> 1) + (x)` = 5

`lim_(x -> 1^-) f(x) ≠ lim_(x -> 1^+) f(x)`

∴ `f` is discountinuous at `x` = 1

At `x` = 2

`lim_(x - 2) f(x)` = 5, f(2) = 5

∴ `f` is continuous at `x` = 2.