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

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- $loga^n=nloga$
- 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=$(-2,\infty)$

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