If $f (x) = x - | x |$ , then $f (x)$ is:

differentiable

\forall x \in R

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continuous

\forall x \in R

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non-differentiable at

x = 0

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discontinuous at

x = 0

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Solution

The correct options are
B continuous $\forall x \in R$
C non-differentiable at $x = 0$
$f (x) = x - | x |$
For $x \geq 0$ ,
$f (x) = 0$
For $x < 0$ ,
$f (x) = 2 x$
The left hand limit and right limits are equal at $x = 0$ . The function is continuous at $x = 0$ .
At $x = 0$ ,
$L . H . D = 2$ , $R . H . D = 0$
Hence, the function is not differentiable at $x = 0$

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If f(x)=x−|x|, then f(x) is:

The correct options are B continuous ∀x∈R C non-differentiable at x=0f(x)=x−|x|For x≥0, f(x)=0For x<0, f(x)=2xThe left hand limit and right limits are equal at x=0. The function is continuous at x=0. At x=0, L.H.D=2 , R.H.D=0Hence, the function is not differentiable at x=0

If $f (x) = x - | x |$ , then $f (x)$ is: