Give the answers of the following questions :
(i) If f(x) = [x] + 2, then find the possible value (s) of f(x) + f(-x).
(ii) If 4[x] = [x + 3], then find x.

Explanation

(i) f(x) + f(-x) = ([x] + 2) + ([-x] + 2) = [x] + [-x] = 4
Now, [x] + [-x] = 0, if x is an integer hence f(x) + f(-x) = 4
But [x] + [-x] = -1, if x is not an integer, then f(x) + f(-x) = -1 + 4 = 3
(ii) 4[x] = [x+3]
`rArr 4[x] = [x] + 3`
`rArr 3[x] = 3`
`rArr [x] = 1`
Hence, `1 le x lt 2`.