Jawaban:

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

Penjelasan dengan langkah-langkah:

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