Question

Diketahui fungsi [tex]f(x) = x²+ x[/tex] dan [tex]g(x) = \frac{2}{x} + 3[/tex]. Tentukan hasil operasi [tex](fog)(-1)[/tex]!​

Answer 1

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f(x) = x² + x

g(x) = 2/x + 3

(f o g)(x) = f(g(x))

(f o g)(x) = f(2/x + 3)

(f o g)(x) = (2/x + 3)² + 2/x + 3

(f o g)(x) = 2/x(2/x + 3) + 3(2/x + 3) + 2/x + 4

(f o g)(x) = 4/x² + 6/x + 6/x + 9 + 2/x + 4

(f o g)(x) = 4/x² + 12/x + 2/x + 9 + 4

(f o g)(x) = 4/x² + 14/x + 13

(f o g)(-1) = 4/(-1)² + 14/(-1) + 13

(f o g)(-1) = 4/1 + 14/(-1) + 13

(f o g)(-1) = 4 + (-14) + 13

(f o g)(-1) = 4 - 14 + 13

(f o g)(-1) = 4 - 1

(f o g)(-1) = 3

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