Respuesta :
The correct answers are x≠2 and x≠(-2).
Domain restrictions are any points in the domain where the function will not have a value. This basically means that it's a point where x won't work in the function.
For the numerator, any value will work for x. We can have a value of 0 in the numerator, or a positive, negative, or decimal number.
However, the denominator cannot equal 0. This is because a fraction bar represents division, and we cannot divide by 0. The values that make the denominator 0 can be found by:
x²-4=0
Add 4 to both sides:
x²-4+4 = 0+4
x² = 4
Take the square root of both sides:
√x² = √4
x = 2 or x = -2.
Domain restrictions are any points in the domain where the function will not have a value. This basically means that it's a point where x won't work in the function.
For the numerator, any value will work for x. We can have a value of 0 in the numerator, or a positive, negative, or decimal number.
However, the denominator cannot equal 0. This is because a fraction bar represents division, and we cannot divide by 0. The values that make the denominator 0 can be found by:
x²-4=0
Add 4 to both sides:
x²-4+4 = 0+4
x² = 4
Take the square root of both sides:
√x² = √4
x = 2 or x = -2.
Answer:
The restrictions on domain are are: [tex] x \neq -2, x\neq 2[/tex]
Step-by-step explanation:
We are given the following information in the question:
We are given an expression:
[tex]\displaystyle\frac{x^2 + 4x +4}{x^2-4}[/tex]
Simplifying the given fraction, we have,
[tex]\displaystyle\frac{x^2 + 4x +4}{x^2-4}\\\\=\frac{(x+2)^2}{(x+2)(x-2)}\\\\=\frac{(x+2)(x+2)}{(x+2)(x-2)}[/tex]
The domain is basically collection of all values of x such that the expression is defined.
We need to make sure that the denominator is not equal to zero for the given fraction.
Thus,
[tex](x+2)(x-2) \neq 0\\\Rightarrow (x+2) \neq 0, (x-2) \neq 0\\\Rightarrow x \neq -2, x\neq 2[/tex]
Hence, the restrictions on domain are are:
[tex] x \neq -2, x\neq 2[/tex]
