Question

If $f\left(x\right)=x^2+2x+2;x\ge -1=-x^3+3x+1;x<-1,$ then the value of $f\left(f\right(-2\left)\right)$ is :

• A. $15$
• B. $17$
• C. $22$
• D. None of these

Answer 1

The correct option is B $17$

$f\left(x\right)=\{\begin{array}{c}{x}^2+2x+2;x⩾-1\\ -x^3+3x+1;x<-1\end{array}$

$f(-2)=-(-2{)}^3+3(-2)+1=8-6+1=3$

$f\left(f\right(-2\left)\right)=f\left(3\right)=(3{)}^2+2(3)+2=17$

Answer option: (B).