Question

I need help with these questions all 3 parts. Please and thank You.

Answer 1

Given:

`f(x)=(x-9)/(x-64)`

The domain of a function is the set of input values for which the function is defined.

For the function f(x), it is undefined when the denominator is zero.

Hence, equating the denominator to zero, we get the undefined points.

`\begin{gathered} x-64=0 \\ x=64 \end{gathered}`

This means there is an undefined point at x = 64

Thus, the domain of the function is all real numbers except 64.

Hence, the domain is;

`x<64\text{ or }x>64`

In interval notation, the domain is;

`(-\infty,64)\cup(64,\infty)`