Multiple choice

Let f: B ® C and g: A ® B be two functions and let h = f o g. Given that h is an onto function. Which of the following is true?

  1. f and g should both be onto functions.

  2. f should be onto but g need not to be onto.

  3. g should be onto but f need not to be onto.

  4. both f and g need not to be onto.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If h = f(g(x)) is onto, then for every element in C, there exists an element in A such that h(a) = c. This implies that f must be able to map to every element in C, so f must be onto; however, g does not need to be onto because f can map the image of g to the entirety of C.

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