Question 1189363
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In the given domain x >= 0, the function is monotonically increasing, 

so it is one-to-one map.


Therefore, the inverse function  {{{f^(-1)(x)}}}  does exist.



The formula for the inverse function is  {{{f^(-1) (x)}}} =  {{{sqrt(x-9)}}},  as you can get it using a backward reasoning.



The domain of f(x) is given in the problem: it is x >= 0.

The range of f(x) is the set of all real numbers >= 9.



The domain of  {{{f^(-1)(x)}}}  is the set of all real numbers  x >= 9.

The range of  {{{f^(-1)(x)}}}  is the set of all real non-negative numbers.
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I answered all the questions, that should be answered.


I leave making plots to you, since it is not a tutors' job.