JEE MAIN - Mathematics (2021 - 25th February Morning Shift - No. 7)
Let f, g : N $$ \to $$ N such that f(n + 1) = f(n) + f(1) $$\forall $$ n$$\in$$N and g be any arbitrary function. Which of the following statements is NOT true?
If g is onto, then fog is one-one
f is one-one
If f is onto, then f(n) = n $$\forall $$n$$\in$$N
If fog is one-one, then g is one-one
Explanation
$$f(n + 1) = f(n) + 1$$
$$f(2) = 2f(1)$$
$$f(3) = 3f(1)$$
$$f(4) = 4f(1)$$
.....
$$f(n) = nf(1)$$
$$f(x)$$ is one-one
$$f(2) = 2f(1)$$
$$f(3) = 3f(1)$$
$$f(4) = 4f(1)$$
.....
$$f(n) = nf(1)$$
$$f(x)$$ is one-one
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