Exponential function:
[tex]\begin{gathered} f(x)=a^x \\ \\ a>0 \\ a\ne1 \end{gathered}[/tex]When you restrict the a to be a positive number (a>0) the domain of the function is all real numbers.
If the value of a is negative then the function is undefined for -1< x < 1.
Then, the given statement is true