A function f:[-5,9] R is defined as follow: f(x)= ll 6 x+1 ; & -5… - Vidyadip

Question

A function $f:[-5,9] \rightarrow R$ is defined as follow:
$f(x)=\left\{\begin{array}{ll}6 x+1 ; & -5 \leq x<2 \\5 x^2-1 ; & 2 \leq x<6 \\3 x-4 ; & 6 \leq x \leq 9\end{array} \text { Find } f(7)-f(1)\right.$

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Answer

$f(x)=6 x+1 ; x=\{-5,-4,-3,-2,-1,0,1\}$
$f(x)=5 x^2-1 ; x=\{2,3,4,5\}$
$f(x)=3 x-4 ; x=\{6,7,8,9\}$
$f(7)-f(1)$
$f(x)=3 x-4$
$f(7)=3(7)-4=21-4=17$
$f(x)=6 x+1$
$f(1)=6(1)+1=6+1=7$
$f(7)-f(1)=17-7=10$

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