SOLUTION: Find a symbolic representation for q^-1(x)
identify the domain and rage of q^-1(x)
q(x)=(x-2)^2, x>_ 2
Either I was out to lunch for this one or I am making it way to hard..
Algebra.Com
Question 328864: Find a symbolic representation for q^-1(x)
identify the domain and rage of q^-1(x)
q(x)=(x-2)^2, x>_ 2
Either I was out to lunch for this one or I am making it way to hard...
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Step 1: Note the domain, 
, the 
being specified as part of the function definition, and the range \,|\,q(x)\,\in\,\mathbb{R},\,q(x)\,\geq\,0\})
Step 2: Replace )
with 
^2)
Step 3: Solve for in terms of 
Only the positive square root because of the 
restriction.
Step 4: Swap variables and replace with )
\ =\ \sqrt{x}\ +\ 2)
The domain of the inverse is the range of the original function. The range of the inverse is the domain of the original function.
Domain: 
Range: \,|\,q^{-1}(x)\,\in\,\mathbb{R},\,q^{-1}(x)\,\geq\,2\})
John
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