The following graph depicts function f(x) in the domain of x andisin; [andminus;2,2]To describe the value of f(x) for integers, a blue filled circle is given. For example, f(0) = 0, f(1) = 1.Which of the following represents f(x)?Here [x] : Greatest integer function. It is defined as the greatest integer less than or equal to x {x} : Fractional part function. It is defined as x - [x]a)[x] - {x}b)[x] + {x}c)x-{x}d)x+{x}Correct answer is option 'A'. Can you explain this answer?

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The following graph depicts function f(x) in the domain of x ∈ [−2,2]

To describe the value of f(x) for integers, a blue filled circle is given. For example, f(0) = 0, f(1) = 1.

Which of the following represents f(x)?

Here [x] : Greatest integer function. It is defined as the greatest integer less than or equal to x

{x} : Fractional part function. It is defined as x - [x]

a)
[x] - {x}
b)
[x] + {x}
c)
x-{x}
d)
x+{x}

Correct answer is option 'A'. Can you explain this answer?

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Verified Answer

The following graph depicts function f(x) in the domain of x ∈ [&...

Graph of [x] is

Graph of {x} is

When we subtract the second graph from the first, we can see that the graph we get is the same as mentioned in the question.

Hence, [x] - {x} , Option A.

Alternate method:

To find the answer, we can also insert values in the functions mentioned.

For the graph given in the question, the value of the function at x=1.5 is 0.5. We can find this by looking at the x and y coordinates of a point in the graph.

Checking the options, we get

A: [x]=1 ; {x}=0.5
1-0.5=0.5: Equal to the one in the given graph.

B: 1+0.5=1.5: hence eliminated

C:1.5-0.5=1: hence eliminated.

D:1.5+0.5=2: hence eliminated

Hence, [x] - {x} , Option A.

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The following graph depicts function f(x) in the domain of x ∈ [−2,2]To describe the value of f(x) for integers, a blue filled circle is given. For example, f(0) = 0, f(1) = 1.Which of the following represents f(x)?Here [x] : Greatest integer function. It is defined as the greatest integer less than or equal to x {x} : Fractional part function. It is defined as x - [x]a)[x] - {x}b)[x] + {x}c)x-{x}d)x+{x}Correct answer is option 'A'. Can you explain this answer?

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