is this a function. ? y^9=x^2+5

Expert Answers
justaguide eNotes educator| Certified Educator

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.

tonys538 | Student

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.