Jawab:

[1.] Range = {-5, -3, -1, 1, 3}

[2.] Range = 5 ≤ f(x) ≤ 29

[3.] Range = 0 ≤ g(x) ≤ 32

[4.] (gof)(x) = 6x²+15x-33

[5.] (gof)(4) = 3

[6.] (gof)(x) = 18x²-36x+11

Penjelasan dengan langkah-langkah:

[1.]  f(x) = 2x-5,  Range

{(2(0)-5), (2(1)-5), (2(2)-5), (2(3)-5), (2(4)-5)} =

{(0-5), (2-5), (4-5), (6-5), (8-5)} =

Range = {-5, -3, -1, 1, 3}

[2.]  f(x) = 4x + 9,  Range

f(x) Min.  4(-1)+9 = 9-4 = 5

f(x) Maks. 4(5)+9 = 20+9 = 29

Range = 5 ≤ f(x) ≤ 29

[3.]  g(x) = 2x² - 4x + 2

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

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

Range ?

g(x) Min.   2((-3(-3-2))+1) = 2((-3(-5))+1) = 2(15+1) = 2(16) = 32

g(x) Maks. 2((1(1-2))+1) = 2((1(-1))+1) = 2(-1+1) = 2(0) = 0

Range = 0 ≤ g(x) ≤ 32

[4.] f(x) = 2x² + 5x - 7    g(x) = 3x-12

(gof)(x) = g(f(x)) = 3(2x²+5x-7)-12 = 6x²+15x-21-12 = 6x²+15x-33

[5.]  f(x) = x+5,  g(x) = x-6

(gof)(4) = (x+5)-6 = (4+5)-6 = 9-6 = 3

[6.] f(x) = 3x-4  g(x) = 2x²+4x-5, tentukan (gof)(x)

g(f(x)) = 2(3x-4)²+4(3x-4)-5 = 2(9x²-24x+16)+12x-16-5 =

18x²-48x+32+12x-16-5 = 18x²-36x+11

____ KLF _____