Question

Given h(x). Determine the value of -2h(-1)+h(3)-4h(2)?
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Answer 1

Given :

$\sf h(x) = \begin{cases} \sf{\sqrt{3 - x}} & \sf x \leq -1 \\ \sf x^{2} - 5x + 2 & \sf -1 < x \leq 2 \\ \sf 7x - 9 & \sf x > 2 \end{cases}$

To Find :

-2 h(-1) + h(3) - 4h(2)

Solution :

Let us find the values of h(x) ,

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• h(-1)

$\to \sf \sqrt{3-(-1)}$

$\to \sqrt{4}$

$\to 2$

• h(3)

$\to 7(3)-9$

$\to 21-9$

$\to 12$

• h(2)

$\to (2)^2-5(2)+2$

$\to 4-10+2$

$\to 6-10$

$\to -4$

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$:\implies \textsf{\textbf{-2h(-1)\ +\ h(3)\ -\ 4h(2)}}\ \; \pink{\bigstar}$

$:\implies \sf -2(2)+(12)-4(-4)$

$:\implies \sf -4+12+16$

$:\implies \sf -4+28$

$:\implies \textsf{\textbf{24}}\ \; \green{\bigstar}$

Answer 2

$\large\underline\blue{\bold{Given \:  Question :-  }}$

$\begin{gathered}\bf h(x) = \begin{cases} \bf{\sqrt{3 - x}} & \sf x \leq -1 \\ \sf x^{2} - 5x + 2 & \bf -1 < x \leq 2 \\ \bf 7x - 9 & \sf x > 2 \end{cases}\end{gathered}$

$\sf \:Determine \: the \: value \: of -2h(-1)+h(3)-4h(2)?$

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$\huge{AηsωeR} ✍$

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$\large\underline\red{\bold{Given :-  }}$

$\begin{gathered}\bf h(x) = \begin{cases} \bf{\sqrt{3 - x}} & \sf x \leq -1 \\ \bf x^{2} - 5x + 2 & \sf -1 < x \leq 2 \\ \bf 7x - 9 & \sf x > 2 \end{cases}\end{gathered}$

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$\large\underline\purple{\bold{To \: Find :-  }}$

$\bf \: -2h(-1) \: + \: h(3) \: - \: 4h(2)$

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$\large\underline\purple{\bold{Solution :- }}$

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$\bf \:Step :- 1.$

$\bf \:  ⟼ Calculation \: of \: h(- 1)$

$\sf \:  ⟼As x = - 1, h(x) = \sqrt{3 - x}$

$\bf\implies \:h( - 1) = \sqrt{3 - ( - 1)} = \sqrt{4} = 2$

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$\bf \:Step :- 2.$

$\bf \:  ⟼Calculation \: of \: h(3)$

$\sf \:  ⟼As x = 3, h(x) = 7x - 9$

$\bf\implies \:h(3) = 7 \times 3 - 9 = 21 - 9 = 12$

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$\bf \:Step :- 3.$

$\bf \:  ⟼ Calculation \: of \: h(2)$

$\sf \:  ⟼As x = 2, h(x) = {x}^{2} - 5x + 2$

$\bf\implies \:h(2) = {2}^{2} - 5 \times 2 + 2 = - 4$

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$\bf \:Step :- 4.$

$\bf \:Now, \: consider : -2h(-1)+h(3)-4h(2)$

☆On substituting the values, we get

$\bf \: = - 2(2) + 12 - 4( - 4)$

$\bf \: = - 4 + 12 + 16$

$\bf \: = 24$

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$\large{\boxed{\boxed{\bf{Hence, -2h(-1)+h(3)-4h(2) = 24}}}}$

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