Question

1.diketahui f(x)=x/3+7,f(x)=2/x dan g(x)=3x+1,maka tentukan (gohof)(x)=
2.diketahui f(x)=2x-5 dan (gof)(x)=8x^2+2x-13,tentukan fungsi g(x)
3.diketahui f^-1(x) =2-3x/4x+5, x# -5/4, maka f(2x-1) =
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Answer 1

Verified answer

Jawab:

komposisi fungsi dan fungsi invers

i) gof(x) = g { f(x) }

ii) f⁻¹(x) = y --> f(y) = x

iii) f(x) =  (ax + b) / (cx + d) --> f⁻¹  (x) = ( -dx + b)/(cx - a)

Penjelasan dengan langkah-langkah:

(2). jika f(x) = 2x - 5

(gof)(x) = 8x² + 2x - 13

g {f(x)} = 8x² + 2x - 13

g (2x - 5) = 8x² + 2x - 13

y = 2x - 5 -->x = 1/2 (y + 5)

g(y) = 8 { 1/2 (y +5)}² + 2 {1/2 (y +5)} - 13

g(y) =  8 (1/4)(y +5)² + (y+5) - 13

g(y) = 2 (y+5)² +(y+5) - 13

g(x) = 2 (x + 5)² + (x + 5) - 13

g(x) = 2(x² +10x + 25) + x + 5 - 13

g(x) = 2x² +20x + 50 + x - 8

g(x)= 2x² + 21x + 42

(3)  f⁻¹ (x) =  (2 -3x)/(4x + 5) = (- 3x + 2) / (4x + 5)

f(x) =  (f⁻¹)⁻¹= { (- 3x + 2) / (4x + 5)}^-1  

f(x)  =  (5x + 2) / (4x + 3), dengan  x ≠  - ³/₄

untuk

f(2x + 1) =  { 5(2x+1) + 2 } / { 4 (2x + 1) + 3 }

f(2x + 1) = (10x + 5 +2 ) / (8x + 4 + 3)

f(2x + 1) = (10x + 7)/(8x + 7)