Question

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of (f/g)(x)?

a) all real values of x
b) all real values of x except x = 5
c) all real values of x except x = –5
d) all real values of x except x = 5 and x = –5

Answer 1

choice b. is right because for x=5 will result this fraction undefined bc than for x=5 the denominator will be equal zero

Answer 2

b) all real values of x except x = 5

Explanation:

Given functions,

`f(x) = x^2 - 25`

`g(x) = x-5`

`((f)/(g))(x)=(f(x))/(g(x))`

By substituting the values,

`((f)/(g))(x)=(x^2-25)/(x-5)`

Which is a rational function,

Since, a rational function is defined for all real values except those for which the denominator = 0,

That is,

x - 5 = 0

⇒ x = 5

Hence, the domain of (f/g)(x) are all real values of x except x = 5 ,

Option b) is correct.