Identify the restrictions on the domain of f(x) = quantity x minus 3 over quantity x plus 5. x ≠ 5 x ≠ −5 x ≠ 3 x ≠ −3

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 :

In this question we need to determined the restrictions on the domain of equation .

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).

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x ≠ - 5

Step-by-step explanation:

Given

f(x) =

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