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Let N be the set of natural numbers and f : N->N be a function given by f(x)=x+1 for `x in N`.Which one of the following is correct?a. f is one-one and ontob. f is one-one but not ontoc. f is only ontod. f is neither one-one nor onto |
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Answer» A function, `f(x)` is a one-one function if`f(a) = f(b)`, then, `a =b` Here, `f(x) = x+1` `f(a) = a+1` `f(2) = b+1` If, `f(a) = f(2)` Then, `a+1 = b+1 => a = b` So, `f(x)` is a one-one function. For a function `f(x)` to be an onto function, it should cover all elements of `x`. Here, as `x in N`. So, `x = (1,2,3,4...) `. `f(x) in N`. `f(x) = (2,3,4,5...)`. As `f(x)` does not have value `1` that is present in `x`, so, `f(x)` is not an onto function. So, option `B` is the correct answer. |
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