imo class 12 relations and functions

Let f(x) = eˣ and g(x) = log(x) for x > 0. The value of f(g(5)) + g(f(3)) is:

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Let f(x) = eˣ and g(x) = log(x) for x > 0. The value of f(g(5)) + g(f(3)) is:

  • A. 8
  • B. 15
  • C. 2
  • D. 0

Answer: A) 8

Explanation: f(g(x)) = e^(log x) = x, so f(g(5)) = 5. g(f(x)) = log(eˣ) = x, so g(f(3)) = 3. Their sum is 5 + 3 = 8.

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