SOLUTION: if f(x)=x^2+9 for x>0 A) Find the inverse showing work B) What is the range of f? I need to know how to do this, please help.

Algebra ->  Functions -> SOLUTION: if f(x)=x^2+9 for x>0 A) Find the inverse showing work B) What is the range of f? I need to know how to do this, please help.      Log On


   

Question 443206: if f(x)=x^2+9 for x>0
A) Find the inverse showing work
B) What is the range of f?
I need to know how to do this, please help.
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse, solve for x and then switch x and y.
y=+x%5E2+%2B+9
y-9+=+x%5E2
0%2B-+sqrt%28y-9%29+=+x
Switch the variables (ignore 0, its there as a placeholder)
y+=+0%2B-+sqrt%28x-9%29
What values of x make this undefined? Well, in order for this function to be defined, x-9%3E+0. So x+%3C9 will give us undefined values. Thus the domain is x%3E9
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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%3E9, then the range of our original function would be y%3E9.
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Hope this helped!