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

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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: