Answer:
∴ y² = x + 3 is not a function
Step-by-step explanation:
* Lets explain how to solve the problem
- The definition of the function is every input (x) has only one
output (y)
- Ex:
# y = x + 1 where x ∈ R , is a function because every x has only
one value of y
# y² = x where x ∈ R , is not a function because y = ±√x, then one
x has two values of y
* Lets solve the problem
∵ y² = x + 3
- Find y by taking √ for both sides
∴ y = ± √(x + 3)
- That means y = √(x + 3) and y = - √(x + 3)
∵ (x + 3) must be greater than or equal zero because there is no
square root for negative number
∴ x + 3 ≥ 0 ⇒ subtract 3 from both sides
∴ x ≥ -3
∴ x must be any number greater than or equal -3
- Let x = 0
∴ y = √(0 + 3) = √3 and y = - √(0 + 3) = -√3
∴ x = 0 has two values of y ⇒ y = √3 and y = -√3
- Any value of x greater than or equal 3 will have two values of y
∴ y² = x + 3 is not a function
