12. Jika f(2x+1) = 4x2 – 8x + 5, maka f(x) = …. A. x2 + 10x – 6 B. x2 – 6x + 10 C. x2 – 3x + 4 D. x2 + 2x – 3 E. x2 + 4x + 4 mohon jwb

Kelas 10 Matematika
Bab Fungsi Komposisi

f(2x + 1) = 4x² - 8x + 5
f(2 . x/2 + 1) = 4 . (x/2)² - 8 . (x/2) + 5
f(x + 1) = 4 . x²/4 - 4x + 5
f(x - 1 + 1) = (x - 1)² - 4 (x - 1) + 5
f(x) = x² - 2x + 1 - 4x + 4 + 5
f(x) = x² - 6x + 10

misalkan...

2x + 1 = a
2x = a-1
x = (a - 1)/2

f(2x + 1) = 4x^2 - 8x + 5

[tex]f(a) = 4( { \frac{a - 1}{2} )}^{2} - 8( \frac{a - 1}{2} ) + 5 \\ \\ = 4 \frac{(a - 1 {)}^{2} }{ {2}^{2} } - 4(a - 1) + 5 \\ \\ = {a}^{2} - 2a + 1 - 4a + 4 + 5 \\ \\ = {a}^{2} - 6a + 10 \\ \\ maka f(x) \\ \\ f(x) = {x}^{2} - 6x + 10[/tex]
B ===>>>> Rock it