Question

How do you find the equation for the inverse of `y=x^2+2, x>=0`?

Answer 1

See explanation.

Explanation:

To find the inverse function of `y=f(x)` you have to transform the formula to calculate `x` in terms of `y`.

`y=x^2+2`

`x^2=y-2`

`x=sqrt(y-2)`

Now we can change the letters to follow the convention that `x` is the independent variable and `y` is the function's value:

`y=sqrt(x-2)`

You have to calculate the domain of the result function.

Here you have the expression under square root sign, so the domain is the set where `x-2>=0`

`x-2>=0 => x>=2`

Answer:

The inverse function is:

`f(x)=sqrt(x-2)`

Its domain is:

`D=[2;+oo)`