Funny Functions - SQR and INT !

The Problem :

 

SQR(x) represents the square root of x, so that SQR(1.44) = 1.2, for example.

INT(x) represents the integer part of x, so that INT(5.73) = 5.

 1.  Which of the following are always true, which are sometimes true, and which are never true?  Give a proof of your assertions if you can, or some examples if not.

            (i)   SQR(x + 4) = SQR(x) + 4

            (ii)  INT(x + 4) = INT(x) + 4

            (iii)  INT(x + 7.5) = INT(x) + 7.5

(iv)  SQR(xy) = SQR(x) SQR(y)

(v)  INT(xy) = INT(x) INT(y)

 

2.  Draw the graph of y = INT(3x) 3 INT(x)  for values of x from 0 to 6. 

3.  For what values of x is it true that INT(SQR(x))  = SQR(INT(x))?

 

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Last modified: June 18, 2007