Use the functions \(\displaystyle{f{{\left({x}\right)}}}={\left({\frac{{{1}}}{{{8}}}}\right)}{x}-{3}\) and \(\displaystyle{g{{\left({x}\right)}}}={x}^{{{3}}}\)

Colten Welch

Colten Welch

Answered question

2022-04-11

Use the functions f(x)=(18)x3 and g(x)=x3 to
find the given value (g1f1)(3)

Answer & Explanation

Ouhamiptkg

Ouhamiptkg

Beginner2022-04-12Added 18 answers

Step 1: Given that
Use the functions f(x)=(18)x3 and g(x)=x3 to
find the given value (g1f1)(3)
Step 2: Solve
First finding f1
We have, f(x)=18x3
Suppose
y=x83
y+3=x8
x=8(y+3)
f1(x)=8(x+3)
Similary,
We have,
g(x)=x3
Suppose,
t=x3
x=(t)13
g1(x)=x13
Step 3: FInding the Pesult
We have,
(g1f1)(x)=g1(f1(x))
=(8(x+3))13
=2(x+3)13
Hence,
(g1f1)(3)=2(3+3)13
=2(0)
=0
Ouhamiptkg

Ouhamiptkg

Beginner2022-04-13Added 18 answers

Step 1
We know that f(f1(x))=x
Therefor we have,
f(f1(x))=f1(x)83=x
f1(x)83=x
Add 3 on both sides, To get
f1(x)8=x+3
Multiply both sides by 8, To get
f1(x)=8x+24
Step 2
We know that g(g1(x))=x
Therefore we have,
g(g1(x))=(g1(x))3=x
Take cube root on both sides, To get
g1(x)=x13
g1f1=g1(f1(x))=(f1(x))13
=(8x+24)13
=(8(x+3))13
=813(x+3)13
g1f1=2(x+3)13
g1f1(1) by g1f1(3)
g1f1(1)=0

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