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Mathematical Statement

54 what are r...

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54 what are rational and irrational functions ?

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Q. If functions

f (x)

g (x)

R \to R

f (x) = x + 3, x

\in

= 4 x, x

\in

g (x) = x + \sqrt{5}

\in

= - x, x

\in

(f - g) (x)

If $f (x)$ and $g (x)$ are real function defined by
$f (x) = {\begin{matrix} x, x i s r a t i o n a l 0, x i s i r r a t i o n a l \end{matrix}$ and $g (x) = {\begin{matrix} 0, x i s r a t i o n a l x, x i s i r r a t i o n a l \end{matrix}$ ,
then $(f - g) (x)$ is

Q. If the functions

f

g

R \to R

f (x) = {\begin{matrix} 0, if x is rational x, if x is irrational \end{matrix}

g (x) = {\begin{matrix} 0, if x is irrational x, if x is rational \end{matrix},

(f - g) (x)

Q. Which of the following is a true statment?
(a)

π and \frac{22}{7}

are both rationals
(b)

π and \frac{22}{7}

are both irrationals
(c)

π

is rational and

\frac{22}{7}

is irrational
(d)

π

is irrational and

\frac{22}{7}

x

y

are two rational and irrational numbers respectively then which of the following are necessarily irrational.

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Standard XII Mathematics