Question

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

• A. $x$
• B. 1
• C. $f\left(x\right)$
• D. $g\left(x\right)$

Answer 1

The correct option is B 1

$g\left(x\right)=1+x-\left[x\right]$ is greater than 1 since
$x-\left[x\right]>0$
$\Rightarrow f\left\{g\right(x\left)\right\}=1$ since $f\left(x\right)=1$ for all
$x>0$
Therefore, (b) is the answer.