Question

Is y= +-sqrt x a function why or why not

Answer 1

Explanation:

No, y = ±√(x) is not a function. Here's why:

A function has a unique output for every single input. In this case, for any given value of x, the equation y = ±√(x) gives two possible outputs, a positive and a negative square root. For example, if x = 4, the equation would yield both y = 2 and y = -2.

This violates the fundamental principle of a function, where each input maps to a unique output. Therefore, y = ±√(x) is not considered a function but rather a relation.

Answer 2

No,
`\sf y =\pm √(x)` is not a function because it has two possible outputs for a single input.

Explanation:

A function is a mathematical relationship where for each input (x-value), there is exactly one output (y-value). However, in the equation
`\sf y = \pm √(x)` , for a single input (x-value), there are two possible outputs:

`\sf √(x)` and
`\sf - √(x)`

Therefore, we have two distinct y-values for the same x-value, violating the fundamental definition of a function.

So,
`\sf y =\pm √(x)` is not a function.