Question

*f(x) = | x – 5 | is*
1️⃣ continuous at point 5 2️⃣ continuous for all real numbers 3️⃣ discontinuous at point 5​

Answer 1

steps

We know that the greatest integer function is discontinuous at integer values. For a value of x just smaller than 5, the greatest integer smaller than it is 4. So,

limx→5−[x]=4

f(x=5)=[5]=5

For a value of x just bigger than 5, the greatest integer smaller than it is 5. So,

limx→5+[x]=5

Since limx→5−f(x)=f(5), the function is not left continuous.

Since limx→5+f(x)=f(5), the function is right continuous.

Answer 2

Answer:

Option-A

Continuous At Point 5

Step-by-step explanation:

GIVEN- f(x) = | x – 5 |

TO FIND- continuous at which point

CONCEPT - f(x)= LHS= RHS that means it wil be continuous

SOLUTION - x – 5= 0

x= 5

At a point -

f(x)= 5

f(x)= | x – 5 |

f(x)= |5-5|

f(x)= 0

this is first equation

at LHS-

f(x)= LHS= lim- f(5) = | x – 5 |

f(x)= |5-5|

f(x)= 0

second equation

at RHS-

f(x)= RHS= lim- f(5) = | x – 5 |

f(x)= |5-5|

f(x)= 0

third equation

from equation First second and third we get that -

f(x)= LHS= RHS= 5

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