Minta tolong dong kaka ​

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Minta tolong dong kaka ​

Minta tolong dong kaka ​

SOAL A.

(fog)(x) = f(g(x))

(fog)(x) = f(x² + 1)

(fog)(x) = (x² + 1) – 1

(fog)(x) = x² + 1 – 1

(fog)(x) = x² + 0

(fog)(x) = x²

————————————————————

(gof)(x) = g(f(x))

(gof)(x) = g(x – 1)

(gof)(x) = (x – 1)² + 1

(gof)(x) = (x² – x – x + 1) + 1

(gof)(x) = (x² – 2x + 1) + 1

(gof)(x) = x² – 2x + 1 + 1

(gof)(x) = x² – 2x + 2

SOAL B.

Misalkan, y = g(x)

y = (x² + 1)

x² = y – 1

x = sqrt{y - 1}

{g}^{ - 1} (x) = sqrt{x - 1}

Penjelasan dengan langkah-langkah:

f(x) = x - 1

g(x) = {x}^{2} + 1

:

(f circ g) = f(g(x)

= ( {x}^{2} + 1 )- 1

= {x}^{2} +1 - 1

= {x}^{2}

:

(g circ f)(x) = g(f(x))

= {(x - 1)}^{2} + 1

= ( {x}^{2} - 2x + 1) + 1

= {x}^{2} - 2x + 1 + 1

= {x}^{2} - 2x + 2

:

g(x) = {x}^{2} + 1

y = {x}^{2} + 1

{y}^{2} + 1 = x

{y}^{2} = x - 1

y = sqrt{x - 1}

{g}^{ - 1} (x) = sqrt{x - 1}