Question

Find domain and range of the function $f\left(x\right)=3^{x+2}$.

• A. Domain $=R-\left\{0\right\}$ and range $=\{x\in R|x<0\}$
• B. Domain $=R-\left\{0\right\}$ and range $=\{x\in R|x>0\}$
• C. Domain $=R$ and range $=\{x\in R|x<0\}$
• D. Domain $=R$ and range $=\{x\in R|x>0\}$

Answer 1

Answer: (D)

Domain $=R$ and range $=\{x\in R|x>0\}$

Clearly we can put any value of $x$ in the function .So domain of the function is $x\in R$

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

For the function in $y$ to be defined $y>0$

So the range of the function is $x\in R$ for $x>0$

So option $D$ is correct.