Let N be the set of natural numbers and let \(f : N \to N\) be defined by \(f(x) = 3x + 2\). Then f is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → one-one but not onto
f is one-one when \(f(a) = f(b)\) forces \(a = b\):
\(3a + 2 = 3b + 2\)
\(3a = 3b\)
\(a = b\)
f is onto when every natural number is the image of some natural number. The smallest value of f is
\(f(1) = 3 \times 1 + 2 = 5\)
So 1, 2, 3 and 4 are not images. For example, \(3x + 2 = 1\) gives
\( \displaystyle x = -\frac{1}{3} \)
which is not a natural number. Hence f is one-one but not onto.