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General

Easy

Question

The function $f colon R rightwards arrow R g colon R rightwards arrow R$ are defined as follows $f left parenthesis x right parenthesis equals 0 left parenthesis x$ is rational $right parenthesis comma g left parenthesis x right parenthesis equals negative 1 left parenthesis x$ is rational $right parenthesis equals$ $1 left parenthesis x$ is irrational $equals 0$ ( $x$ is irrational $right parenthesis$ then fog $left parenthesis pi right parenthesis plus g o f invisible function application left parenthesis e right parenthesis$

-1
0
1
2

The correct answer is: -1

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$f colon R rightwards arrow R$ and $g colon R rightwards arrow R$ are given by $f left parenthesis x right parenthesis equals vertical line x vertical line$ and $g left parenthesis x right parenthesis equals left square bracket x right square bracket$ for each $x element of R$ then $x element of R colon g left square bracket f left parenthesis x right parenthesis right square bracket less or equal than f left square bracket g left parenthesis x right parenthesis right square bracket$

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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 $fraction numerator p over denominator q end fraction element of Q$
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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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