Find the domains of following functions fx-2xlog 2x-3x-1-x-1

f(x)=2^xlog(2x)+3x+1|x| 1 For existance of f,(1)2x gt;0=x gt;0 (2)x≠± 1 ⇒ x∈ R {1} { 1} Domain =R {1, 1} ...

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Standard XII

Mathematics

Definition of Functions

Find the doma...

Question

Find the domains of following functions $f (x) = \frac{2^{x}}{log (2 x)} + \frac{3 x + 1}{| x | - 1}$

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Solution

$f (x) = \frac{2^{x}}{log (2 x)} + \frac{3 x + 1}{| x | - 1}$
For existance of $f, (1) 2 x > 0 = x > 0$
$(2) x \neq \pm 1$
$\Rightarrow x \in R - {1} - {- 1}$
Domain $= R - {1, - 1}$

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Find the domains of following functions f(x)=2xlog(2x)+3x+1|x|−1

f(x)=2xlog(2x)+3x+1|x|−1For existance of f,(1)2x>0=x>0(2)x≠±1⇒x∈R−{1}−{−1}Domain =R−{1,−1}

Find the domains of following functions $f (x) = \frac{2^{x}}{log (2 x)} + \frac{3 x + 1}{| x | - 1}$

$f (x) = \frac{2^{x}}{log (2 x)} + \frac{3 x + 1}{| x | - 1}$
For existance of $f, (1) 2 x > 0 = x > 0$
$(2) x \neq \pm 1$
$\Rightarrow x \in R - {1} - {- 1}$
Domain $= R - {1, - 1}$