SOLUTION: Can you help me on this inverse funtions question: 1)Determine the inverse of each of the following functions. State the domain and range of the inverse. For which of these is t

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Question 204306: Can you help me on this inverse funtions question:
1)Determine the inverse of each of the following functions. State the domain and range of the inverse. For which of these is the inverse also a function?
a)f(x)=2(x-2)^2
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the inverse of each of the following functions. State the domain and range of the inverse. For which of these is the inverse also a function?
a)f(x)=2(x-2)^2
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1st: Interchange x and y to get:
x = 2(y-2)^2
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2nd: Solve for "y":
(y-2)^2 = (x/2)
y-2 = sqrt(x/2) or y-2 = -sqrt(x/2)
y = 2+sqrt(x/2) or y = 2-sqrt(x/2)
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The inverse is not a function because there are two y-values for
each value of "x".
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Domain of the inverse: Since x/2 must not be negative the domain is
All Real Numbers greater than or equal to zero.
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Range of the inverse: Since the domain of the given function is
all Real Numbers, the range of the inverse is all Real Numbers.
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Cheers,
Stan H.
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