Question

Sa se expliciteze E(x) =|x-2|+|3x|

Answer 1

Explicație pas cu pas:

E(x) = |x-2| + |3x|

$x - 2 = 0 \implies x = 2$

$3x = 0 \implies x = 0$

$|x-2| = \begin{cases} 2 - x, \ x < 2 \\ x - 2, \ x \geqslant 2\end{cases}$

$|3x| = \begin{cases} -3x, x < 0 \ \\ 3x, x \geqslant 0 \ \end{cases}$

=>

$E(x) = \begin{cases} 2 - x - 3x, x < 0 \ \\ 2 - x + 3x, 0 \leqslant x < 2 \ \\ x - 2 + 3x, \ x \geqslant 2 \end{cases}$

$\iff E(x) = \begin{cases} 2(1 - 2x), x < 0 \ \\ 2(x + 1), 0 \leqslant x < 2 \ \\ 2(2x - 1), \ x \geqslant 2 \end{cases}$