jika f(x) = x + 5 dan (g o f) (x) = 2x^2 + 5x + 6. maka nilai (f o g) (1) =

[tex]\displaystyle x+5=a\\x=a-5\\\\(g\circ f)(x)=2x^2+5x+6\\g(f(x))=2x^2+5x+6\\g(x+5)=2x^2+5x+6\\g(a)=2(a-5)^2+5(a-5)+6\\g(1)=2(1-5)^2+5(1-5)+6\\g(1)=2(-4)^2+5(-4)+6\\g(1)=2(16)-20+6\\g(1)=32-20+6\\g(1)=18\\\\(f\circ g)(1)=f(g(1))\\(f\circ g)(1)=f(18)\\(f\circ g)(1)=18+5\\\boxed{\boxed{(f\circ g)(1)=23}}[/tex]

Matematika X SMA
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Pembahasan :
Gof(x) = 2x² + 5x + 6
G(f(x)) = 2x² + 5x + 6
G(x + 5) = 2x² + 5x + 6

Misal x + 5 = a
x = a - 5

Sehingga...
G(a) = 2(a - 5)² + 5(a - 5) + 6
G(a) = 2(a² - 10a + 25) + 5a - 19
G(a) = 2a² - 15a + 31
G(x) = 2x² - 15x + 31

Fog(x) = f(g(x))
Fog(1) = f(g(1))
Fog(1) = f[2(1)² - 15(1) + 31]
Fog(1) = f[2 - 15 + 31]
Fog(1) = f(18)
Fog(1) = 18 + 5
Fog(1) = 23