Question

If $f\left(x\right)=\{\begin{array}{c}1+\left|x\right|;\\ \left[x\right];\end{array}\begin{array}{c}x<-1\\ x\ge -1\end{array}$ Also, [.] is greatest interger function then $f\left(f\right(-2.4\left)\right)$ is equal to

• A. $-3$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $-3$

$f\left(x\right)=\{\begin{array}{ccc}1+|x|& ;& x<-1\\ \left[x\right]& ;& x⩾-1\end{array}$

$\begin{array}{cc}f(-2.3)=1+|-2.3|& =1+2.3\\ & =3.3\end{array}$

$\begin{array}{cc}f\left(f\right(-2.3\left)\right)& =f\left(3.3\right)\\ & =\left[3.3\right]=3\\ \text{Hence,}\left(c\right)& \text{is the correct option.}\end{array}$