Question

Which of the following option(s) is/are correct for exponential function $f\left(x\right)=a^x$ ?

• A. Domain of $f\left(x\right)$ is $R$
• B. Range of $f\left(x\right)$ is $(0,\infty )$
• C. $a\in R-\{0,1\}$
• D. $a\in (0,1)\cup (1,\infty )$

Answer 1

Answer: (A), (B), (D)

$a\in (0,1)\cup (1,\infty )$

For $f\left(x\right)=a^x$ to be an exponential function,
$a>0$ and $a\ne 1$
Clearly, domain is $R$
Since, $a>0\Rightarrow a^x>0$
Therefore, range is $(0,\infty )$