F(x)= 8 4x , amp; 8 4x≥0 (8 4x) , amp; 8 4x lt;0 ⇒ f(x)= 8 4x , amp; 8≥4x 4x 8 , amp; 8 lt;4x ⇒ f(x)= 8 4x , amp; x≤2 4x 8 , amp; x ...

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Absolute Value Function

If fx=|8-4x|,...

Question

If $f (x) = | 8 - 4 x |,$ then

f (x) = 8 - 4 x

when

x \geq 2

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f (x) = 8 - 4 x

when

x \leq 2

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f (x) = 4 x - 8

when

x > 2

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f (x) = 4 x - 8

when

x < 2

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Solution

The correct option is C $f (x) = 4 x - 8$ when $x > 2$
$f (x) = {\begin{matrix} 8 - 4 x, & 8 - 4 x \geq 0 - (8 - 4 x), & 8 - 4 x < 0 \end{matrix}$
$\Rightarrow f (x) = {\begin{matrix} 8 - 4 x, & 8 \geq 4 x 4 x - 8, & 8 < 4 x \end{matrix}$
$\Rightarrow f (x) = {\begin{matrix} 8 - 4 x, & x \leq 2 4 x - 8, & x > 2 \end{matrix}$

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