Question

Let g(x) = 1 + x - [x] and f(x)=$\{\begin{array}{cc}-1,& x<0\\ 0,& x=0\\ 1,& x>0\end{array}$, then for all x, f(g(x)) is equal to

• A. x
• B. 1
• C. f(x)
• D. g(x)

Answer 1

The correct option is B 1

Here g(x) = 1 + n - n = 1, $x=n\in Z$

$1+n+k-n=1+k(wheren\in Z,0<K<1)$

Now$f\left(g\right(x\left)\right)=\{\begin{array}{cc}-1,& g\left(x\right)<0\\ 0,& g\left(x\right)=0\\ 1,& g\left(x\right)>0\end{array}$

Clearly, $g\left(x\right)>0$ for all x. So, f(g(x)) = 1 for all x.