Question

Identify the restrictions on the domain of f(x) = quantity x plus 5 over quantity x minus 2. x ≠ 5 x ≠ −5 x ≠ 2 x ≠ −2

Answer 1

Answer: Third option.

Step-by-step explanation:

By definition, Rational Functions have the following form:

$f(x)=\frac{P(x)}{Q(x)}$

Where $P(x)$ and $Q(x)$ are polynomials.

The Restrictions of the Domain of Rational Functions are those Real numbers that make the denominator equal to zero, because the division by zero is not defined.

 In this case, you have the following Rational Function:

$f(x)=\frac{x+5}{x-2}$

The Restrictions of the Domain can be found applying this steps:

- Make the denominator equal to 0:

$x-2=0$

- Solve for "x":

$x=2$

Then, the Domain of this function includes all "x" not equal to 2.

Therefore,  the answer is:

$x\neq 2$