Jika f(x)=2x-1, g(x)=7+3x, dan h(x)= 5x, carilah: a) (f-1 o g-1 o h-1 ) (x) b) (f o g o h)-1 (x) Tolong dijawab yaa
Matematika
vianing
Pertanyaan
Jika f(x)=2x-1, g(x)=7+3x, dan h(x)= 5x, carilah:
a) (f-1 o g-1 o h-1 ) (x)
b) (f o g o h)-1 (x)
Tolong dijawab yaa
a) (f-1 o g-1 o h-1 ) (x)
b) (f o g o h)-1 (x)
Tolong dijawab yaa
1 Jawaban
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1. Jawaban finala1
cari inversnya satu satu
f(x) = 2x-1
y=2x-1
2x=y+1
x=(y+1)/2
f-1(x)=(x+1)/2
g(x)=7+3x
y=7+3x
3x=y-7
x=(y-7)/3
g-1(x)=(x-7)/3
h(x)=5x
y=5x
x=y/5
h-1(x)=x/5
f-1 o g-1 o h-1 (x) = f-1(g-1(h-1(x)))
=f-1(g-1(x/5))
=f-1(((x/5)-7)/3)
samakan penyebut
=f-1((x-35)/5 x 1/3)
=f-1((x-35)/15)
=(((x-35)/15)+1)/2
samakan penyebut
=(x-20)/15 x 1/2
=(x-20)/30
(fogoh)-1(x)
=h-1 o g-1 o f-1(x)
=h-1 (g-1 ((x+1)/2))
=h-1((((x+1)/2)-7)/3)
=h-1((x-13)/6)
=(x-13)/30
maaf jika ada kesalahan