Functions 2 Question 8

9.

Let g(x)=1+x−[x] and f(x)= {−1x<0,0x=0,1x>0} then for all x,f[g(x)] is equal to

(a) x

(b) 1

(c) f(x)

(d) g(x)

(2001, 1M)

Show Answer

Answer:

Correct Answer: 9. (b)

Solution:

  1. g(x)=1+x−[x] is greater than 1

since x−[x]>0

f[g(x)]=1, since f(x)=1 for all x>0

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