"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 $(f \pm g)(x) = f(x) \pm g(x),(f/g)x = {{f(x)} \over {g(x)}}$"

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Accepted Answer

"$f + g = \sqrt x + \sqrt {1 - x}$

$\Rightarrow x \ge 0$ & $1 - x \ge 0 \Rightarrow x \in [0,1]$

$f - g = \sqrt x - \sqrt {1 - x}$

$\Rightarrow x \ge 0$ & $1 - x \ge 0 \Rightarrow x \in [0,1]$

$f/g = {{\sqrt x } \over {\sqrt {1 - x} }}$

$\Rightarrow x \ge 0$ & $1 - x > 0 \Rightarrow x \in [0,1)$

$g/f = {{\sqrt {1 - x} } \over {\sqrt x }}$

$\Rightarrow 1 - x \ge 0$ & $x > 0 \Rightarrow x \in (0,1]$

$g - f = \sqrt {1 - x} - \sqrt x$

$\Rightarrow 1 - x \ge 0$ & $x \ge 0 \Rightarrow x \in [0,1]$

$\Rightarrow$ $x \in (0,1)$"

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

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

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Drill 25 more like these. Every day. Free.

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