SOLUTION: Domain and range of inverse f(x)=6-x^2;x >= 0

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Question 169960: Domain and range of inverse f(x)=6-x^2;x >= 0
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
First we need to find the domain and range of

Domain: Given

Range: (use a graph)

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Finding the Inverse:

Start with the given function

Replace f(x) with y

Switch x and y. The goal is to solve for y

Subtract 6 from both sides

Multiply both sides by -1

Rearrange the terms

Take the square root of both sides. Note: since the domain of f(x) is , this means that we're only considering the positive square root.

So the answer is which means that the inverse function is

Now the domain and range of the inverse is simply the reverse of the domain and range of the original function

So the domain and range of is:

Domain:

Range: