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# If $f:A\rightarrow B$, $3^{f(x)}+2^{-x}=4$ and $f(x)$ is bijection then the domain $A$ of $f(x)$ is ?

$\begin{array}{1 1} (-2 ,\infty) \\ (-3, \infty) \\ (-1,1) \\ (-2,2) \end{array}$

Toolbox:
• $loga^n=nloga$
• Domain of $f(x)$ is set of all possible values of x for which $f$ is defined.
Given: $3^{f(x)}+2^{-x}=4$
$\Rightarrow\:3^{f(x)}=4-2^{-x}$
Taking log on both sides we get
$f(x)log3=log(4-2^{-x})$
$\Rightarrow\:f(x)=\large\frac{log(4-2^{-x})}{log3}$
$\Rightarrow\:4-2^{-x} >0$
$\Rightarrow\:2^2>2^{-x}$
$x>-2$
Domain=$(-2,\infty)$
edited May 19, 2014