Question

ES PARA MAÑANA AYUDAAAAAAAAAAAAAAAAA POR FAVOOOOOOOOOOOOOOOOOOOOOOR
Halla el rango de las siguientes funciones afines:
g(x) = -0,5x - 3 y D(g) = {x/x ∈ Z ; 2 ≤ x ≤ 6}
h(x) = -4x + 2.5 y D(h) = {x/x ∈ R ; 0 ≤ x ≤ 5}

Answer 1

Respuesta:

Explicación paso a paso:

[tex]g(x)= -0.5x-3[/tex]   ;  D(g) = { x/x ∈ Z ; 2 ≤ x ≤ 6 }

Rango:

Despejamos " x ".

[tex]0.5x = -g(x)-3[/tex]

[tex]x = \frac{-g(x)}{0.5} -\frac{3}{0.5} = -2g(x) -6[/tex]

[tex]2\leq x\leq 6, entonces: 2\leq -2g(x)-6\leq 6[/tex]

[tex]2+6\leq -2g(x)-6+6\leq 6+6[/tex]

[tex]8\leq -2g(x) \leq 12[/tex]

[tex]Rango: R(g) = [ -4,-6][/tex]

[tex]-1 ( 8\leq -2g(x)\leq 12),entonces: -8\geq 2g(x) \geq -12[/tex]

[tex]\frac{-8}{2} \geq \frac{2g(x)}{2} \geq \frac{-12}{2}[/tex]

[tex]-4\geq g(x) \geq -6[/tex]

[tex]Rango: R (g) = [ -6, -4][/tex]

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[tex]h(x) = -4x+2.5[/tex]     ;    [tex]D(h) =[/tex] { x / x ∈ R ; 0 ≤ x ≤5 }

Rango:

Despejamos " x " .

[tex]4x = 2.5-h(x)[/tex]

[tex]x = \frac{2.5-h(x)}{4}[/tex]

[tex]x = \frac{5}{8} -\frac{h(x)}{4}[/tex]

[tex]0 \leq \frac{5}{8} -\frac{h(x)}{4} \leq 5[/tex]

[tex]-8 ( 0\leq \frac{5}{8} -\frac{h(x)}{4} \leq 5),entonces: 0\geq -5+2h(x)\geq -40[/tex]

[tex]0+5\geq -5+5+2h(x)\geq -40+5[/tex]

[tex]5\geq 2h(x)\geq -35[/tex]

[tex]\frac{5}{2} \geq \frac{2h(x)}{2} \geq \frac{-35}{2}[/tex]

[tex]2.5\geq h(x) \geq -17.5[/tex]

[tex]Rango: R(h) = [ -17.5, 2.5][/tex]