Question

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

Answer 1

`x\in(-\infty, \infty)` & `f(x)\in (0, \infty)`

Explanation:

For the given function: `f(x)=10^x`

`LHL=RHL=f(x)`

i.e. `f(x)=10^x` is continuous everywhere hence its domain the set of real numbers i.e.

`x\in\mathbb R` or `x\in (-\infty, \infty)`

Now, range of function is determined as

`\lim_{x\to -\infty}f(x)=\lim_{x\to -\infty}10^x=0`

`\lim_{x\to \infty}f(x)=\lim_{x\to \infty}10^x=\infty`

hence the range of function `f(x)=10^x` is `(0, \infty)`