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 with explanation:

The given logarithmic function whose base is, 7 is

       $y=f(x)=\log_{7}x$

Domain of a function is defined as, set of all possible values of , x , for which ,y is defined.

$\log_{7}x=\frac{\log x}{\log 7}$

 is defined for,

→ log x > 0.

⇒ x ∈ (0,∞)

And range of a function is defined as those values of y, for which x, is defined.

$y=\log_{7}x\\\\y=\frac{\log x}{\log 7}\\\\ \log x =y \log 7\\\\x=7^y$

So, Range = y∈ (0,∞).

The inverse of the above function can be obtained by, replacing, x by y, and y by x , in the above equation:

   So, the inverse of the above function is :

           $y=7^x$

Here, x ∈ (0,∞) and, y ∈ (0,∞).

Answer 2

I hope this helps you out