The domain of a function f(x) is all the values of x for which f(x) is a determinate quantity.

Here f(x) = 5 / (5x - 7)

f(x) is not defined for 5x - 7 = 0

=> 5x = 7

=> x = 7/5

**Therefore the domain of the function is all values of x except x = 7/5.**

To determine the domain of f(x) = 5/5x-7).

The domain of the function f(x) = 5/(5x-7) is is all the set of values of the variable x for which the f(x) is defined.

We see that 5/(5x-7) is defined for all real values of x except for 5x-7 = 0, as 5 divided by zero does not exist.

Therefore the value of x for which 5x-7 = 0 is excluded from all the real values x can take. So x = 7/5 is not admissible.

so the domain of f(x) is set of all points {x: - infinity< = x = < infinity} - {x = 7/5}.

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}.**