Question

The real function F(x) = [x] 1 point %3D .where x is real number and [x] denotes greatest integer fnction is​

Answer 1

Answer:

Let f(x)=∣[x]x∣ for −1≤x≤2 , where [x] denotes greatest integer function, then

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ANSWER

We divide the interval in 4 parts,

For −1<x<0

f(x)=−x

For 0<x<1

f(x)=0

For 1<x<2

f(x)=x

For x=2

f(x)=4

Now at x=0,

lim x →0

−

f(x) = 0 = lim x →0

+

f(x)

Hence, f(x) is continuous at x = 0

At x = 1

lim x →1

−

f(x) = 0 not equal to lim x →1

+

f(x)

Hence, f(x) is discontinuous at x = 1

At x = 2

lim x →2

−

f(x) = 0 not equal to lim x = 2 f(x)

Hence, f(x) is discontinuous as well as non-differentiable at x=2

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Answer 2

Answer:

Given, [x]

2

+2[x]=3x

Case 1. when 0≤x<1⇒[x]=0

∴3x=0+0⇒x=0

Case 2. when 1≤x<2⇒[x]=1

∴3x=1+2⇒x=1

Case 3. when x=2⇒[x]=2

∴3x=2

2

+2.2=8⇒x=8/3



=2

Hence solution is {0,1}