F(x)= 2x^3+x 7 , amp; 2x^3+x 7≥0 (2x^3+x 7) , amp; 2x^3+x 7 lt;0 ⇒ f(x)= 2x^3+x 7 , amp; 2x^3+x 7≥0 7 2x^3 x , amp; 2x^3+x 7 lt;0 nbsp; ...

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Absolute Value Function

If fx=|2x3+x-...

Question

If $f (x) = | 2 x^{3} + x - 7 |,$ then

f (x) = 2 x^{3} + x - 7

when

2 x^{3} + x - 7 \geq 0

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f (x) = 2 x^{3} + x - 7

when

2 x^{3} + x - 7 \leq 0

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f (x) = 7 - 2 x^{3} - x

when

2 x^{3} + x - 7 < 0

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f (x) = 7 - 2 x^{3} - x

when

2 x^{3} + x - 7 > 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is C $f (x) = 7 - 2 x^{3} - x$ when $2 x^{3} + x - 7 < 0$
$f (x) = {\begin{matrix} 2 x^{3} + x - 7, & 2 x^{3} + x - 7 \geq 0 - (2 x^{3} + x - 7), & 2 x^{3} + x - 7 < 0 \end{matrix}$
$\Rightarrow f (x) = {\begin{matrix} 2 x^{3} + x - 7, & 2 x^{3} + x - 7 \geq 0 7 - 2 x^{3} - x, & 2 x^{3} + x - 7 < 0 \end{matrix}$

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