Shea V

16 November 2024 23:49

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Shea V

16 November 2024 23:49

Pertanyaan

1. jika f(x) = 2-3x dan g(x) = 2x-1, fungsi komposisi (f°g) (x) 2. diketahui f(x)= 2x-5 dan g(x) = x²+3x-2. nilai (g°f)(4)=

1. jika f(x) = 2-3x dan g(x) = 2x-1, fungsi komposisi (f°g) (x)

2. diketahui f(x)= 2x-5 dan g(x) = x²+3x-2. nilai (g°f)(4)=

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Fadila H

17 November 2024 04:43

Jawaban terverifikasi

<p>1. f(x)=2-3x dan g(x) =2x-1</p><p>f°g(x) =f(g(x))&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=2-3(2x-1)&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=2-6x+3</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=5-6x</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=-6x+5</p><p>&nbsp;</p><p>2.f(x) =2x-5 dan g(x) =x²+3x²-2</p><p>g°f(x) =g(f(x))&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=x(2x-5)²+3(2x-5) -2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=(4x²-20x+25) +6x-15-2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=4x²-20x+6x+25-15-2</p><p>g°f(x) =4x²-16x+8</p><p>g°f(4) =4(4)² - 16(4) +8</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=64 &nbsp; &nbsp; - 56 &nbsp; &nbsp; &nbsp; +8</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;=16</p>

1. f(x)=2-3x dan g(x) =2x-1

f°g(x) =f(g(x)) 

           =2-3(2x-1) 

           =2-6x+3

           =5-6x

           =-6x+5

 

2.f(x) =2x-5 dan g(x) =x²+3x²-2

g°f(x) =g(f(x)) 

           =x(2x-5)²+3(2x-5) -2

           =(4x²-20x+25) +6x-15-2

           =4x²-20x+6x+25-15-2

g°f(x) =4x²-16x+8

g°f(4) =4(4)² - 16(4) +8

           =64     - 56       +8

           =16


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