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

Question

7844 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-30T06:54:42

See 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: