Question

A function $f:[-7,6)\to R$ is defined as follows
$f\left(x\right)=\{\begin{array}{cc}{x}^2+2x+1;& -7\le x<-5\\ x+5;& -5\le x\le 2\\ x-1;& 2<x<6\end{array}$
(iii) $2f(-4)+3f\left(2\right)$
(ii) $f(-7)-f(-3)$
(iv) $\frac{4f(-3)+2f\left(4\right)}{f(-6)-3f\left(1\right)}$

Answer 1

$f(-4)=-4+5=1f\left(2\right)=2+5=7\therefore 2f(-4)+3f\left(2\right)=2+21=23$

$f(-7)={(-7)}^2+2(-7)+1=36f(-3)=-3+5=2\therefore f(-7)-f(-3)=36-2=34$

$f\left(4\right)=4-1=3f(-6)={(-6)}^2+2(-6)+1=25f\left(1\right)=1+5=6\therefore \frac{4f(-3)+2f\left(4\right)}{f(-6)-3f\left(1\right)}=\frac{8+6}{25-18}=2$