If gx=1+x-x and fx=-1,x<00,x=01,x>0then for all x, fgx is equal to
x
1
fx
gx
Explanation for the correct option:
Finding the value of fgx:
Given that,
gx=1+x-x,
Any whole number can be written as
x=x+x
⇒x-x=x...1
fgx=-1,gx<00,gx=01,gx>0=-1,1+x-x<00,1+x-x=01,1+x-x>0=-1,1+x<00,1+x=01,1+x>0from1
We know that,
x∈[0,1)
So,
fgx=-1,x<-10,x=-11,x>-1
Here, only x>-1∈[0,1) .
Therefore, the value of fgx is 1.
Hence, the correct option is B.