Ace Test Series: Set Theory & Algebra - Functions

Question

I thought answer would be (C). Because, inner 'f' is outputting values 8, 9, 3, 1, 2. So, outer 'f' should take these values for final output. But as these values are not in its domain [S], so that should be undefined.. Right?

Answer 1

You are correct. C is correct answer, but because of same explanation, B should also be correct answer.

gof(x) = g(f(x))

On computing f(x), it gives output that belongs to the set T. This output serves as input of g(x). But the valid domain set for g(x) is S, while it is receiving its input in domain T, hence we say that gof(x) is not defined too.

Comments

I think I am wasting my time running through such test series..