Return to Assignments Logarithmic functions and graphs

### Assignment 7

Draw the graph of the function:

### Solution

The function exists if both logarithms exist. The first is defined for , thus for or . We know this because the quadratic function can be factorized:

The second logarithm is defined for , thus the function as a whole is defined for .

Now the function can be written as:

We can sketch this graph more easily than the graph of the original function, but the graph is only valid for :