Question

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

ANSWER IS -
The domain of f is x > 0.
The range of f is all real numbers.
The domain of the inverse function is all real numbers.
The range of the inverse function is y > 0.
The domain of f is the same as the
range of the inverse function.
The range of f is the same as the
domain of the inverse function.

Answer 1

The domain of f is x > 0.

The range of f is all real numbers.

The domain of the inverse function is all real numbers.

The range of the inverse function is y > 0.

The domain of f is the same as the

range of the inverse function.

The range of f is the same as the

domain of the inverse function.

Answer 2

• The domain of f is x > 0.

• The range of f is all real numbers.

and

• The domain of f is the same as the range of the inverse function.

• The range of f is the same as the domain of the inverse function.

Explanation:

All log functions without any additional terms added to it outside the operation have domain x>0 and all real number range.

When the inverse is found, (x,y) are switched to (y,x). This measn the range becomes the domain the domain becomes the range.