Question

Find the domain of (fx)=log5 (9-2x)

Answer 1

To find the domain of the given function, we have to take into account that the value inside the parenthesis can not be less than or equal to 0, this is because 5 can not be raised to an exponent and obtain 0 or a less number than 0 as result.

We can use this information to find the domain of f(x). Remember that 9-2x has to be greater than 0:

`\begin{gathered} 9-2x>0 \\ -2x>-9 \\ x<(-9)/(-2) \\ x<4.5 \end{gathered}`

It means that x has to be less than 4.5. Then, the domain of the function is:

`D=(-\infty,4.5)`