# What is the domain and range of  f (x) =10^x?

$x \setminus \in \left(- \setminus \infty , \setminus \infty\right)$ & $f \left(x\right) \setminus \in \left(0 , \setminus \infty\right)$

#### Explanation:

For the given function: $f \left(x\right) = {10}^{x}$

$L H L = R H L = f \left(x\right)$

i.e. $f \left(x\right) = {10}^{x}$ is continuous everywhere hence its domain the set of real numbers i.e.

$x \setminus \in \setminus m a t h \boldsymbol{R}$ or $x \setminus \in \left(- \setminus \infty , \setminus \infty\right)$

Now, range of function is determined as

$\setminus {\lim}_{x \setminus \to - \setminus \infty} f \left(x\right) = \setminus {\lim}_{x \setminus \to - \setminus \infty} {10}^{x} = 0$

$\setminus {\lim}_{x \setminus \to \setminus \infty} f \left(x\right) = \setminus {\lim}_{x \setminus \to \setminus \infty} {10}^{x} = \setminus \infty$

hence the range of function $f \left(x\right) = {10}^{x}$ is $\left(0 , \setminus \infty\right)$