Answer:
x ≠ - 5
Step-by-step explanation:
Given
f(x) = [tex]\frac{x-3}{x+5}[/tex]
The denominator of f(x) cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the value that x cannot be.
solve : x + 5 = 0 ⇒ x = - 5 ← excluded value
This question is based on the concept of restriction of domain.Therefore, the correct option is (b) that is x ≠ −5 (x is not equal to -5).
Given that equation is :
[tex]f(x) = \dfrac{x-3}{x+5}[/tex]
In this question we need to determined the restrictions on the domain of equation [tex]f(x) = \dfrac{x-3}{x+5}[/tex] .
According to question,
Therefore. x is equal to +3 or -3 is included in domain because, at both values function is defined.
By putting +5 in given function, function gives definite value.Therefore, x = ++5 is also included in domain.
By putting x = -5 in numerator and in denominator , We get definite value from numerator that is 2. But in denominator we get 0.
Therefore, denominator is equal to 0 when x = -5 . Hence the function is not defined. Thus, x = -5 is not included in domain.
Therefore, the correct option is (b) that is x ≠ −5 (x is not equal to -5).
For more details, prefer this link;
https://brainly.com/question/16776761
