SOLUTION: 1 a)Is the function f(x) = x^2 +9,x ≥ 0 one-to-one? If so, find f^-1 and justify your answer. b)Graph f, f^−1,and y=x on the same coordinate axes. Also state domain and rang

Algebra ->  Functions -> SOLUTION: 1 a)Is the function f(x) = x^2 +9,x ≥ 0 one-to-one? If so, find f^-1 and justify your answer. b)Graph f, f^−1,and y=x on the same coordinate axes. Also state domain and rang      Log On


   

Question 1189363: 1 a)Is the function f(x) = x^2 +9,x ≥ 0 one-to-one? If so, find f^-1 and justify your answer.
b)Graph f, f^−1,and y=x on the same coordinate axes. Also state domain and range of f and f^-1.
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Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

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

so it is one-to-one map.


Therefore, the inverse function  f%5E%28-1%29%28x%29  does exist.



The formula for the inverse function is  f%5E%28-1%29+%28x%29 =  sqrt%28x-9%29,  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%5E%28-1%29%28x%29  is the set of all real numbers  x >= 9.

The range of  f%5E%28-1%29%28x%29  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.