Diketahui f(x) 2X + 3 dan g(x) +x2tentukan rumus (gof) -1 (X)*​

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Diketahui f(x) 2X + 3 dan g(x) +x2tentukan rumus (gof) -1 (X)*​

Penjelasan dengan langkah-langkah:

f(x) = 2x + 3

g(x) = x²

gof(x)

= g(f(x))

= g(2x + 3)

= (2x + 3)²

= 4x² + 12x + 9

Maka,

gof(x) = 4x² + 12x + 9

y = 4x² + 12x + 9

y – 9 = 4x² + 12x

y – 9 + (3/2)² = 4x² + 12x + (3/2)²

y – 27/4 = (2x + 3/2)²

sqrt{y - 27/4} = (2x + 3/2)

sqrt{y - 27/4} – 3/2 = 2x

x = frac{sqrt{y - 27/4} - 3/2}{2}

  = frac{-3 + sqrt{y - 27} }{4}

Sehingga,

(gof)⁻¹(x) = frac{-3 + sqrt{x - 27} }{4}