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

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Answer 1 · 2018-07-12T22:08:49

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

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)#