JEE MATHEMATICS MCQ: FUNCTIONS

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Analyzing +4 | -1

If the functions are defined as

f(x) = \sqrt x

and

g(x) = \sqrt {1 - x}

, then what is the common domain of the following functions?

f + g,\,\,f - g,\,\,f/g,\,\,g/f,\,\,g - f

, where

(f \pm g)(x) = f(x) \pm g(x),(f/g)(x) = \frac{{f(x)}}{{g(x)}}

View answer and explanation

Correct option: C

0 < x < 1

Option C (0 < x < 1) is correct because it represents the intersection of the domains of f(x) and g(x), excluding points where either function is undefined.

More Questions from FUNCTIONS

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

, where

f(x)=x(4-x)

, then

f^{-1}(x)

is given by: If

g(f(x))=|\sin x|

and

f(g(x))=(\sin \sqrt{x})^2

, then Let

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

be defined by

f\left( x \right) = x - \left[ x \right]

, then

{f^{ - 1}}\left( x \right)

equals Let

f: R \rightarrow R

be defined as

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

f(x)=(x+1)^2-1(x \geq-1)

. Then the set

S=\left\{x: f(x)=f^{-1}(x)\right\}

contains