Diketahui fungsi f(x) = 2x + 1 dan g(x) = x² − 3x + 3. Jika nilai (gof)(t) = 7 maka nilai t adalah …
Diketahui:
=> f(x) = 2x + 1
=> g(x) = x² - 3x + 3
Ditanya:
=> Jika nilai (gof)(t) = 7 maka nilai t adalah?
Penyelesaian:
- Cari dulu (g o f)(x)
=> (g o f)(x) = (x² - 3x + 3) o (2x + 1)
=> (g o f)(x) = (2x + 1)² - 3(2 x 1) + 3
=> (g o f)(x) = 4x² + 4x + 1 - 6x - 3 + 3
=> (g o f)(x) = 4x² - 2x + 1
- Jadi, nilai t adalah
=> (g o f)(t) = 4t² - 2t + 1
=> 7 = 4t² - 2t + 1
=> 0 = 4t² - 2t - 6
4t² - 2t - 6 = 0 ➡️ Sederhanakan => bagi kedua ruas dengan 2
[tex]2 {t}^{2} - t - 3 = 0 [/tex]
[tex](2t \: - 3)(t + 1) = 0[/tex]
[tex]2t - 3 = 0[/tex]
[tex]2t = 3[/tex]
[tex]t = \frac{3}{2} [/tex]
[tex]t + 1 = 0[/tex]
[tex]t = - 1[/tex]
Kesimpulan:
=> Jadi, nilai t adalah -1 atau 3/2
dik : f(x) = 2x + 1
g(x) = x² − 3x + 3
(gof)(t) = 7
dit : t?
jawab :
(gof) (x) = f(x) o g(x)
(gof) (x) = (2x + 1) o (x^2 - 3x + 3)
(gof) (x) = (2x + 1)^2 - 3 (2x + 1) + 3
(gof) (x) = 2x^2 + 2x + 2x + 1^2 - 6x - 3 + 3
(gof) (x) = 4x² - 2x + 1
(gof)(t) = 4t² - 2t + 1
7 = 4t² - 2t + 1
4t² - 2t + 1 - 7 = 0
4t² - 2t - 6 = 0
( 4t - 6 ) (t + 1) = 0
- 4t - 6 = 0
- 4t = 6
- t = 6/4 = 3/2
- t + 1 = 0
- t = -1
jadi nilai t adalah -1 atau 3/2
[answer.2.content]
