Jawaban:

1.10

2.64

3.ada di langkah2

4.5

5.1

Penjelasan dengan langkah-langkah:

Diketahui

f(x) = x + 4

g(x) = x² + 1

h(x) = 5x

Pertama, cari dulu (g o f)(x)

(g o f)(x) = (x² + 1) o (x + 4)

(g o f)(x) = (x + 4)² + 1

(g o f)(x) = x² + 8x + 16 + 1

(g o f)(x) = x² + 8x + 17

Kemudian, cari fungsi (h o g o f)(x)

(h o g o f)(x) = h(x) o (g o f)(x)

(h o g o f)(x) = 5x o (x² + 8x + 17)

(h o g o f)(x) = 5(x² + 8x + 17)

(h o g o f)(x) = 5x² + 40x + 85

Jadi, Nilai (h o g o f)(-3) adalah

(h o g o f)(-3) = 5(-3)² + 40(-3) + 85

(h o g o f)(-3) = 45 - 120 + 85

(h o g o f)(-3) = 10

→ Jawaban 10

2.f(x) = 2x + 4 g(x) = 3x dan h(x) = x² + 1

a. (f○G○h)(x) = f○g(x² + 1).

= f(3(x² + 1))

= f(3x² + 3)

= 2(3x² + 3) + 4

= 6x² + 10

b. (f○g○h)(3) = 6 . 3² + 10

= 64

3.3 (x/x+1) -2..

3x/x+1 (-2)

disamakan penyebutnya (3x - 2(x+1) per x + 1)

3x - 2x - 2 per x+ 1 hasilnya x - 2 per x+1.

4.diket:

f(x) = x - 1

g(x) = x² + 2x - 3

ditanya:

gof(3)....?

jawab:

- menentukan fungsi gof(x) lebih dlu

 gof(x) = g(f(x))

 gof(x) = (x - 1)² + 2(x - 1) - 3

           = x² - 2x + 1 + 2x - 2 - 3

           = x² - 4

- menentukan nilai gof(3)

  gof(x) = x² - 4

  gof(3) = (3)² - 4

             = 9 - 4

             = 5

Kesimpulan

Jadi, nilai dari gof(3) adalah 5.

5.f(x) = x + 2

g(x) = x² - 3x + 1

h(x) = 2x - 1

a. (hogof)(x)

cari (gof)(x) dahulu

(gof)(x)

= ( x + 2 )² - 3( x + 2 ) + 1

= x² + 4x + 4 - 3x - 6 + 1

= x² + x - 1

lalu cari (hog)(x)

(hog)(x)

= 2( x² + x - 1 )

= 2x² + 2x - 2

b. (gofoh)(x)

cari (foh)(x)

(foh)(x)

= ( 2x - 1 ) + 2

= 2x + 1

lalu cari (goh)(x)

(goh)(x)

= ( 2x + 1 )² - 3( 2x + 1 ) + 1

= 4x² + 4x + 1 - 6x - 3 + 1

= 4x² - 2x - 1

2. f(x) = x + 3 / x - 4

g(x) = 2x + 1 / x - 4

a. (fog)(x)

= ( 2x + 1 / x - 4 ) + 3 / ( 2x + 1 / x - 4 ) - 4

= 5x - 11 / -2x + 17

b. (fog)-¹(x)

misal f(x) = y

y = 5x - 11 / -2x + 17

y(-2x + 17) = 5x - 11

-2xy + 17y = 5x - 11

-2xy - 5x = -17y - 11

x(-2y - 5) = -17y - 11

x = -17y - 11 / -2y - 5

(fog)-¹(x) = -17x - 11 / -2x - 5

c. (fog)-¹(a) = 4

4 = -17a - 11 / -2a - 5

4(-2a - 5) = -17a - 11

-8a - 20 = -17a - 11

-8a + 17a = -11 + 20

9a = 9

a = 1

nilai a = 1

gambar di atas itu penyelesaian nomor 5

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