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Inverse of a Function

f:Q→ Q is def...

Question

$f : Q \to Q$ is defined by $f (x) = 15 x + 7$ is

A

injective only

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B

surjective only

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C

bijective

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D

neither injective nor surjective

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Solution

The correct option is D bijective
$y = 15 x + 7$ is a linear function.
Since linear functions are bijective, ie. there is only one value of $y$ corresponding to a single value of $x$ , hence $f (x)$ is bijective and invertible.
$x = \frac{y - 7}{15}$
Hence, option 'C' is correct.

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[NCERT EXEMPLAR]

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