Question

Dik: f(x) =2x+1
g(x) =x+3/x²+1
h(x) =√(x)
Tentukan:
A. fogoh(x)
B. gohof(x)
C. hofog(x)
D. fohog(x)
E. gofoh(x)
F. hogof(x)
​

Answer 1

Materi : Fungsi dan Relasi

f(x) = 2x + 1

g(x) = ( x + 3 )/( x² + 1 )

h(x) = √x

_________________/

A. ( f o g o h )(x)

= f(g(h(x)))

= f(g(√x))

= f( [ √x + 3 ]/[ x + 1 ] )

= ( √[ 2x + 1 ] + 3 )/( 2x + 2 )

B. ( g o h o f )(x)

= g(h(f(x)))

= g(h( 2x + 1 ))

= g( √[2x+1] )

= ( √[2x+1] + 3 )/( 2x + 2 )

C. ( h o g o f )(x)

= h(g(f(x)))

= h(g(2x+1)

= h( [ 2x + 4 ]/[ 2x + 2 ] )

= √( [x+2]/[x+1] )

D. ( f o h o g )(x)

= f(h(g(x)))

= f(h( [x+3]/[x²+1] ))

= f( √( [x+3]/[x²+1] ))

= 2√( [x+3]/[x²+1] ) + 1

E. ( g o f o h )(x)

= g(f(h(x)))

= g(f(√x))

= g( 2√x + 1 )

= [ 2√x + 4 ]/[ 4x + 4√x + 2 ]

= [ √x + 2 ]/[ 2x + 2√x + 1 ]

F. ( h o g o f )(x)

= h(g(f(x)))

= h(g( 2x + 1 ))

= h( [ 2x + 4 ]/[ 4x² + 4x + 2 ] )

= √( [x+2]/[2x²+2x+1] )

Semoga bisa membantu

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