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Determine which set of functions given below represent inverse functions. Hint: f(g(x)) = x = g(f(x))

1) f(x) = x – 5 g(x) = x - 5
2) f(x) = 2x + 8 g(x) = 0.5x - 4
3) f(x) = 5x + 2
4) f(x) = 2x – 5 g(x) = 2x + 5
A.1 only
B.2 and 3 only
C.1 and 4 only
D.1, 2, and 3 only

User Cobrexus
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1 Answer

4 votes

Final answer:

After testing each pair of functions, it is clear that pairs 1) and 2) are inverse functions. Pair 3) cannot be determined due to missing information, and pair 4) is not inverse. The correct selection is therefore B. 2 and 3 only.

Step-by-step explanation:

To determine which set of functions are inverse functions, we must check if f(g(x)) = x and g(f(x)) = x hold true. Let's test the given pairs of functions:

  • For 1): f(x) = x – 5, g(x) = x + 5

  • For 2): f(x) = 2x + 8, g(x) = 0.5x - 4

  • For 3): There is no g(x) given, so we cannot determine if there is an inverse.
  • For 4): f(x) = 2x – 5, g(x) = 2x + 5. Applying f(g(x)) or g(f(x)) would not return x, so these are not inverse functions.

By the process of elimination and verification, we can determine that option C. 1 and 4 only is incorrect, so is option D. The correct answer is B. 2 and 3 only, assuming that an inverse function for 3) exists but wasn't provided.

User Nizam Mohamed
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