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

Question

asked May 10, 2017 88.1k views

2 Answers

Chen Levy · Answer 1 · 2017-05-16T04:02:37+0000

1. Find the inverse function:

$y=\log 7x,\\ 7x=e^y,\\ \\ x=(e^y)/(7).$

Rechange x and y, then:

y=(e^x)/(7).

The inverse function is

f^(-1)(x)=(e^x)/(7).

2. The domain of f(x) is the range of
f^(-1)(x) and the range of f(x) is the domain of
f^(-1)(x).

3. The domain of
f^(-1)(x) is
$x\in (-\infty,\infty)$ and the range of
is
$y\in (0,\infty)$ .

Answer: the domain of f(x) is
$x\in (0,\infty)$ and the range of f(x) is
$y\in (-\infty,\infty).$