A relation y = f(x) is a function if for each value of x there is only value of y. For no value of x can there be more than 1 value of x.
y^9 = x^2 + 5
`y = root(9)(x^2 + 5)`
Here, for any value of x there is only one value of y. `y = root(9)(x^2 + 5)` is a function.
y^9 = x^2 + 5 is a function.
A relation between y and x is a function if there is one to one mapping of x and y. For each value of y there should be a corresponding value of x and this value of x should be unique.
For y^9=x^2+5, if both sides are raised to the exponent 1/9
y = `(x^2 + 5)^(1/9)`
Now, the value of x^2 is the same for +-x and for any value of y there is only one value of x that gives that particular value of y.