Estelle V

16 Juli 2025 16:12

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Estelle V

16 Juli 2025 16:12

Pertanyaan

Tolong bantu jawab Materi Fungsi Komposisi Matematika Wajib kelas 11 f(x) = 2x-1 g(x) = x² -3x-10 tentukan (f•g) (x) (g•f) (x) (g•g) (x) Dengan penjelasan lengkap dan bahasa sederhana

Tolong bantu jawab 

Materi Fungsi Komposisi Matematika Wajib kelas 11 

f(x) = 2x-1
g(x) = x² -3x-10
tentukan
(f•g) (x)
(g•f) (x)
(g•g) (x)
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Keanu R

16 Juli 2025 20:18

<p>f(g(x))=2(x^2-3x-10)-1-------&gt;subtitusi</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =2x^2-6x-20-1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =2x^2-6x-21</p><p>g(f(x))=(x+2)(x-5)-------&gt;di faktorkan(x<sup>2</sup>-3x-10)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =(2x-1+2)(2x-1-5)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (2x+1)(2x-6)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =4x<sup>2</sup>-12x+2x-6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =4x<sup>2</sup>-10x-6</p><p>g(g(x))=(x+2)(x-5)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=(x<sup>2</sup>-3x-10+2)(x<sup>2</sup>-3x-10-5)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=(x<sup>2</sup>-3x-8)(x<sup>2</sup>-3x-15)-----------&gt;kali massue</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=x<sup>4</sup>-3x<sup>3</sup>-15x<sup>2</sup>-3x<sup>3</sup>+9x<sup>2</sup>+45x-8x<sup>2</sup>+24x+120</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=x<sup>4</sup>-6x<sup>3</sup>-14x<sup>2</sup>+69x+120</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>

f(g(x))=2(x^2-3x-10)-1------->subtitusi

            =2x^2-6x-20-1

            =2x^2-6x-21

g(f(x))=(x+2)(x-5)------->di faktorkan(x2-3x-10)

            =(2x-1+2)(2x-1-5)

            = (2x+1)(2x-6)

            =4x2-12x+2x-6

            =4x2-10x-6

g(g(x))=(x+2)(x-5)

             =(x2-3x-10+2)(x2-3x-10-5)

             =(x2-3x-8)(x2-3x-15)----------->kali massue

             =x4-3x3-15x2-3x3+9x2+45x-8x2+24x+120

             =x4-6x3-14x2+69x+120

             


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