Answered

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

Aall real values of x
Ball real values of x except x = 5
Call real values of x except x = –5
Dall real values of x except x = 5 and x = –5

Verified Answer :

jhonyy9

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:

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.

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