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

1 Answer

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

Explanation:

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

LHL=RHL=f(x)LHL=RHL=f(x)

i.e. f(x)=10^xf(x)=10x 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)