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Maths-

General

Easy

Question

If $Q$ denotes the set of all rational numbers and $f open parentheses fraction numerator p over denominator q end fraction close parentheses equals square root of p to the power of 2 end exponent minus q to the power of 2 end exponent end root$ for any $fraction numerator p over denominator q end fraction element of$ Q, then observe the following statements
I) $f open parentheses fraction numerator p over denominator q end fraction close parentheses$ is real for each $fraction numerator p over denominator q end fraction element of Q$
II) $f open parentheses fraction numerator p over denominator q end fraction close parentheses$ is a complex number for each $fraction numerator p over denominator q end fraction element of Q$ Which of the following is correct?

Both I and II are true
I is true, II is false
I true, II is false
Both I and II are false

The correct answer is: I true, II is false

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If $Z rightwards arrow Z$ is defined byf $left parenthesis x right parenthesis equals open curly brackets table row cell fraction numerator x over denominator 2 end fraction text if end text x text is even end text end cell row cell 0 text if end text x text odd end text end cell end table close$ then $f$ is

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