Which of the following pair of functions are inverses of each other?

  see below

Step-by-step explanation:

If you can't tell by looking, you can evaluate g(f(x)) = f(g(x)) = x to see if it is true. You can do this using the expressions for f(x) and g(x), or you can do this using some chosen value for x, such as x=0 or x=1 or both.

Using x=0, the answer choices look like ...

  A: f(0) = (∛8)/7 = 2/7. Then g(2/7) = ((7(2/7)-8)³ = -6³ ≠ 0

  B: f(0) = 7·0³ +10 = 10. Then g(10) = ∛((10 -10)/7) = 0 . . . . possible answer

  C: f(0) = 2·0³ +12 = 12. Then g(12) = 12/2 -12 = -6 ≠ 0

  D: f(0) = ∛(0+2) -7 = -7+∛2. Then g(-7+∛2) = (-7+∛2 +2)³ +7 ≠ 0

The only viable choice is B.

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For choice B, we can work out the inverse of f(x) in detail:

  x = f(y) = 7y³ +10 . . . . . solve x=f(y) for y to find the inverse

  x -10 = 7y³ . . . . . subtract 10

  (x -10)/7 = y³ . . . . . divide by 7; next take the cube root

  ∛((x -10)/7) = y . . . . . matches g(x)