UPSEE Solved Model Paper 7

Given:
g (x) = 1 + x - [x] ... (i)
f (x) = {

−1	x<0
0	x=0
1	x>0

... (ii)
W e have to find f (g(X)) .
Now.
g (x) = 1 + x - [x]
= 1 + (X) ... (iii)
[Using definition of fractional part function]
f (g (x)) = f (1 + (x)) [Using (iii)]
Since, 1 ≤ 1 + {x} < 2 , for all x [Since 0 ≤ (x) < 1]
∴ f (1 + (x)) = 1 [Using (ii)]
⇒ f [g(x)] = 1
Hence, option 'B' is correct