Let f, g a: N ® N such that f (n + 1) = f (n) +f (1)
and g be any arbitrary function. Which of the following statements is NOT true?
Let f, g a: N ® N such that f (n + 1) = f (n) +f (1) and g be any arbitrary function. Which of the following statements is NOT true?
Option 1 -
If fog is one – one, then g is one – one
Option 2 -
f is one – one
Option 3 -
If g is onto, then fog is one – one
Option 4 -
If f is onto, then f (n) =
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1 Answer
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Correct Option - 4
Detailed Solution:f : N ->N
f (n + 1) = f (n) + f (1)
Let f (1) = a, a
f (2) = f (1) + f (1) = 2a
f (3) = f (2) + f (1) = 3a
and so on
->f (m) = ma, m, a
->f is one – one, Þ option (2) is true.
Suppose f (g (x) is one-one
then f (g (x1) f (g (x2) for x1
->g (x1)
->g is one – one
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