Question

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.

Answer 1

Answer:

• 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 ...

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

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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.

Answer 2

Answer:

A, D, E

   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:

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