If f : A→B given by


If $f: A \rightarrow B$ given by $3^{f(x)}+2^{-x}=4$ is a bijection, then

(a) $A=\{x \in R:-1

(b) $A=\{x \in R:-3

(c) $A=\{x \in R:-2

(d) None of these


(d) None of these

$f: A \rightarrow B$


$\Rightarrow 3^{f(x)}=4-2^{-x}$

Taking $\log$ on both the sides,

$f(x) \log 3=\log \left(4-2^{-x}\right)$

$\Rightarrow f(x)=\frac{\log \left(4-2^{-x}\right)}{\log 3}$

Logaritmic function will only be defined if $4-2^{-x}>0$

$\Rightarrow 4>2^{-x}$

$\Rightarrow 2^{2}>2^{-x}$

$\Rightarrow 2>-x$


$\Rightarrow x \in(-2, \infty)$

That means $A=\{x \in R:-2

As we know that, $f(x)=\frac{\log \left(4-2^{-z}\right)}{\log 3}$

$\Rightarrow f(x)=1$ which does not belong to any of the options.

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