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

Question

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

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Answer

$f(x)=6 x+1 ; x=\{-5,-4,-3,-2,-1,0,1\}$
$f(x)=5 x^2-1 ; x=\{2,3,4,5\}$
$f(x)=3 x-4 ; x=\{6,7,8,9\}$
$\frac{2 f (-2)- f (6)}{ f (4)+ f (-2)}$
$f(x)=6 x+1$
$f(-2)=6(-2)+1=-12+1=-11$
$f(x)=3 x-4$
$f(6)=3(6)-4=18-4=14$
$f(x)=5 x^2-1$
$f(4)=5(4)^2-1=5(16)-1$
$=80-1=79$
$f(x)=6 x+1$
$f(-2)=6(-2)+1=-12+1=-11$
$\frac{2 f (-2)- f (6)}{ f (4)+ f (-2)}=\frac{2(-11)-14}{79-11}$
$=\frac{-22-14}{68}$
$=\frac{-36}{68}$
$=\frac{-9}{17}$

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