Question 443206
To find the inverse, solve for x and then switch x and y.

{{{y= x^2 + 9}}}
{{{y-9 = x^2}}}
{{{0+- sqrt(y-9) = x}}}
Switch the variables (ignore 0, its there as a placeholder)
{{{y = 0+- sqrt(x-9)}}}
What values of x make this undefined? Well, in order for this function to be defined, {{{x-9> 0}}}. So {{{x <9}}} will give us undefined values. Thus the domain is {{{x>9}}}
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Notice this relationship. The domain of the inverse is the same as the range of the original function.
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If our domain of our inverse is {{{x>9}}}, then the range of our original function would be {{{y>9}}}.
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Hope this helped!