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Definition of Function

If fx and ...

Question

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

A

o n e - o n e a n d o n t o

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B

n e i t h e r o n e - o n e n o r o n t o

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C

o n e - o n e b u t n o t o n t o

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D

o n t o b u t o n e - o n e

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Solution

The correct option is A $o n e - o n e a n d o n t o$

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Similar questions

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}

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}

f : R \to R

g : R \to R

(f - g)

g (x)

be a polynomial of degree one and

f (x)

f (x) = {\begin{matrix} g (x), & x \leq 0 | x |^{s i n x}, & x > 0 \end{matrix}

f (x)

is continuous satisfying

f^{'} (1) = f (- 1)

g (x)

Q. The period of the function

f (x) = {\begin{matrix} 1, & x is rational 0, & x is irrational \end{matrix}

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)

f

g

are real function defined by

f (x) = 2 x - 1

g (x) = x^{2}

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