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In each of the following cases, states w...

In each of the following cases, states whether the function is one-one,
onto or bijective. Justify your answer. `f : R rarr R` defined by f(x) = ` 1 + x^2`

Text Solution

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We have f(-1) = `1+ (-1)^2 = 2` and `f(1) = 1 + 1^2 = 2`
`therefore` f maps both -1 and 1 to 2
`therefore` f is not one-one
Since f(x) = `1 + x^2 `gt` 0` for all `x in R`, negative real numbers do not have pre images under f
`therefore` f is not onto
And hence f is not bijective.
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