contestada

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

Respuesta :

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

shristiparmar1221

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,

  • If we putting the value of x is 3 and -3  in numerator and denominator,we get definite value.

Therefore. x is equal to +3 or -3 is included in domain because, at both values  function is defined.

  • Now checking the value x is equal to +5,

By putting +5 in given function, function gives definite value.Therefore, x = ++5 is also  included in domain.

  • Now at x = -5,

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

Otras preguntas