Test Index

Functions Part 1

Section: Mathematics

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Question : 42 of 100

Marks: +1, -0

If the functions are defined as

f(x)=\sqrt{x}

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

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

f+g, f-g, \frac{f}{g}, \frac{g}{f}, g-f

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

[18 Mar 2021 Shift 1]

$0 \leq x \leq 1$
$0 \leq x< 1$
$0< x< 1$
$0< x \leq 1$

Solution:

Given,

f(x)=\sqrt{x}

and

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

\therefore

Domain of

f(x)=D_{1}

is

x \geq 0

i.e.

D_{1}: x \in (0, \infty)

and domain of

g(x)=D_{2}

is

1-x \geq 0

\Rightarrow \;\; x \leq 1

i.e.

D_{2}: x \in (-\infty

1]

As, we know that, the domain of

f+g, f-g, g-f

will be

D_{1} \cap D_{2}

as well as the domain for

\;\frac{f}{g}

is

D_{1} \cap D_{2}

except all those value(s) of

x

,

such that

g(x)=0 .

Similarly, for

\;\frac{g}{f}

is

D_{1} \cap D_{2}

but

f(x) \neq 0

.

Hence, common domain for

(f+g),(f-g),\left(\;\frac{f}{g}\right),\left(\;\frac{g}{f}\right)

and

(g-f)

will be

0< x< 1

.

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