Question

The domain of definition of the function $y\left(x\right)$ given by $3^x+3^y=3$ is

• A. $(0,1]$
• B. $[0,2]$
• C. $(-\infty ,0]$
• D. $(-\infty ,1)$

Answer 1

Answer: (C), (D)

The correct options are
C $(-\infty ,0]$
D $(-\infty ,1)$

We have

$3^x+3^y=3$

$\Rightarrow 3^y=3-3^x$

$\Rightarrow y={\log }_3(3-3^x)$.

Option (A), (B) can't be true as if $x=1$ the $y=\log 0$, which is undefined.

All other cases i.e. $x\in (-\infty ,0]$ and $x\in (-\infty ,1)$, $y$ is defined.

So, optiion (c) and (d) are correct.