diketahui fungsi f(x)= x^2-2,g(x-1)=2x-1 dan h(x+1)=6-x. Nilai (fogoh)(2) adalah...
Matematika
tasyaaurelliaa
Pertanyaan
diketahui fungsi f(x)= x^2-2,g(x-1)=2x-1 dan h(x+1)=6-x. Nilai (fogoh)(2) adalah...
1 Jawaban
-
1. Jawaban arsetpopeye
f(x) = x^2 - 2
g(x - 1) = 2x - 1 => misal x - 1 = a maka x = a + 1
g(a) = 2(a + 1) - 1 = 2a + 2 - 1 = 2a + 1
g(x) = 2x + 1
=> g(5) = 2(5) + 1 = 11
h(x + 1) = 6 - x => misal x + 1 = a maka x = a - 1
h(a) = 6 - (a - 1) = 6 - a + 1 = 7 - a
h(x) = 7 - x
=> h(2) = 7 - 2 = 5
(f o g o h)(2) = (f o g)(h(2)) = (f o g)(5) = f(g(5)) = f(11) = 11^2 - 2 = 121 - 2 = 119