**7. Find the following values of the greatest integer function.
**

**a) [1/4]**

**b) [-3/4]**

**c) [22/7]**

**d) [-2]**

**e) [[1/2]+ [1/2]]**

**f) [-3+ [-1/2]]**

**Solution: **The greatest integer, denoted by [x], is the largest integer less than or equal to x satisfying the inequation

[x]\leq x < [x]+1

Where x is a real number

**(a)**[1/4]

The greatest integer less than equal to 1/4 is 0

So, [1/4]=0

**(b)**[-3/4]

The greatest integer less than equal to -3/4 is -1

So, [-3/4]=-1

**(c)**[22/7]

The greatest integer less than equal to 22/7 is 3

So, [22/7]=3

**(d)** [-2]

The greatest integer less than equal to -2 is -2 itself

So,[-2]=-2

**(e)** [[1/2]+[1/2]]

The greatest integer less than equal to 1/2 is 0

So, [1/2]=0

Now,

[[1/2]+[1/2]]=[0+0]

=[0]

=0

So, [[1/2]+[1/2]]=0

**(f)** [-3+[-1/2]]

The greatest integer less than equal to -1/2 is -1

So, [-1/2]=-1

Now,

[-3+[-1/2]]=[-3+(-1)]

=[-4]

=-4

So, [-3+[-1/2]]=-4