What is the domain of the function f(x)=5/(5x-7) ?

The domain of a function is the range of x values that
makes the function to exist.

In this case, the expression
of the function is a ratio. A ratio is defined if and only if it's denominator is
different from zero.

We'll impose the constraint of
existence of the function:

5x - 7 different from
0.

Now, we'll put 5x - 7 = 0 to determine those values of x
that have to be rejected from the domain of definition of the given
function.

5x - 7 = 0

We'll
add 7 and we'll get:

5x =
7

We'll divide by 5:

x =
7/5

The domain of definition of the given
function is: (-infinite ; 7/5) U (7/5 ;
+infinite).

We can also write
the domain of the function as the real set of numbers and we'll exclude the value 7/5: R
- {7/5}.