F(x)=x over 5x-7

Question

find the domain of the function using interval notation

Answer 1

f(x) = x/(5x - 7), the function will produce an indeterminate value at 5x - 7 = 0.

 

All other values will produce real numbers. 5x - 7 = 0 -> x = 7/5.

 

the domain of the function includes all the real numbers excluding 7/5.

Answer 2

When dealing with a rational function ( a function that has a variable in the denominator of a fraction), you must insure that the denominator is not zero which would make the fraction undefined.

 

So 5x-7=0 when x=7/5. All other values would lead to a defined fraction.

 

So your answer is all real numbers except x=7/5. In interval notation that's ( - infinity, 7/5) ∪ (7/5, infinity).

 

Hope this helps.