Di ketahui f(x).2x-3

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g(x)=x²+1
tentukan a). (f o g)(x)
b). (g o f)(x)
di ketahui f(x).2x-3 textless br / textgreater g(x)=x²+1 textless br / textgreater tentukan a). (f o g)(x) textless br / textgreater b). (g o f)(x)
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Di ketahui f(x).2x-3

Di ketahui f(x).2x-3

1. a. ( f o g )(x) = f[ g(x) ]

= f( x² + 1 )

= sqrt{2(x + 1) - 3} \ = sqrt{2x + 2 - 3} \ = sqrt{2x - 1}

b. ( g o f )(x) = g[ f(x) ]

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

= 2x + 1 + 1

= 2x + 2

2. ( f o g )(x) = f[ g(x) ]

4x² – 20x + 25 = f( 2x – 5 )

misal : 2x – 5 = R

2x = R + 5

x = frac{r + 5}{2} \ 4( frac{r + 5}{2} ) {}^{2} - 20( frac{r + 5}{2} ) + 25 = f(r) \ 4 (frac{r {}^{2} + 10r + 25}{4} ) - 10(r + 5) + 25 = f(r)

R² + 10R + 25 – 10R – 50 + 25 = f(R)

R² = f(R)

f(x) = x²

3. f(x) = y

frac{3x + 2}{x - 1} = y

3x + 2 = y( x – 1 )

3x + 2 = yx – y

3x – yx = -y – 2

( 3 – y ) x = -y – 2

x = frac{ - y - 2}{3 - y} \ f {}^{ - 1} (x) = frac{ - x - 2}{3 - x}