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

Answer:

b) all real values of x except x = 5

Step-by-step explanation:

Given functions,

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

$g(x) = x-5$

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}$

By substituting the values,

$(\frac{f}{g})(x)=\frac{x^2-25}{x-5}$

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.