Question

What are the domain and range of the logarithmic function f(x) = log7x? Use the inverse function to justify your answers.

Answer 1

Answer:

Step-by-step explanation:

Since log is defined by all positive real  numbers

therefore domain is all  positive real number that is ( 0,∞)

Range is given by real numbers

inverse of the given function is  (10^x)/7

Whose domain is all real numbers and range is all positive real number

And since we know that domain of function and range of its inverse

& range of a function and domain of its inverse is same

which we are getting in the problem

so  answer is justified

Answer 2

Answer:    

Step-by-step explanation: The domain of a function is the set of all values for which the function is defined and the range is the set of all values $y$, for which there exists some $x$ such that

$y=f(x)=\log7x\\\Rightarrow 7x=10^y\\\Rightarrow x=10^y/7$.

Since $log x$ is defined for all real values of $x$ greater than zero. So, the domain of the given function is

D={x|7x is a real number>0}={x|x is a real number>0}.

And range is given by

R={y|y=\log 7x}={y|y is a real number}.

Thus, the domain is the set of all positive real numbers and range is the set of all real numbers.