Mathematics: Aref (x) = StartFraction 1 Over 8 EndFraction x cubed and g (x) = 2 x Superscript one-third inverses of each other? Check all that apply. The simplified expression for f(g(x)) is x. The simplified expression for f(g(x)) is One-fourth x. The simplified expression for g(f(x)) is 2x. The simplified expression for g(f(x)) is x. The functions are inverses of each other. The functions are not inverses of each other.

Aref (x) = StartFraction 1 Over 8 EndFraction x

Ответ:

GalleTF

02.02.2022

The simplified expression for f(g(x)) is x. The simplified expression for g(f(x)) is x. The functions are inverses of each other.

Step-by-step explanation:

Given:

$f(x)=\dfrac{1}{8}x^3\\\\g(x)=2x^{\frac{1}{3}}$

We find that ...

$f(g(x))=\dfrac{1}{8}(2x^{\frac{1}{3}})^3=\dfrac{1}{8}(2^3)(x^{\frac{3}{3}})=\dfrac{8}{8}x\\\\\boxed{f(g(x))=x}\\\\g(f(x))=2\left(\dfrac{1}{8}x^3\right)^{\frac{1}{3}}=2\left(\dfrac{1}{8^{\frac{1}{3}}}\right)(x^{\frac{3}{3}})=\dfrac{2}{2}x\\\\\boxed{g(f(x))=x}$

So, the statements that apply are ...

The simplified expression for f(g(x)) is x. The simplified expression for g(f(x)) is x. The functions are inverses of each other.

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Ответ:

elizabethhubbe

20.09.2022

Mathematics

25 gallons

Step-by-step explanation:

The van needs 1 gallon of gas to travel 30 miles so that would mean that 25 gallons of gas would be needed to travel 750 miles.

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