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Question 518618: f(x)=3 Sqrt 3x-4
inverse function is f^-1(x)=
Domain of f
Range of f
Domain of f^-1
Range of f^-1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! f(x)=3 Sqrt(3x-4)
inverse function is f^-1(x)=
Domain of f
Range of f
Domain of f^-1
Range of f^-1
**
y=3√(3x-4)
interchange x and y
x=3√(3y-4)
x/3=√(3y-4)
square both sides
x^2/9=3y-4
3y=x^2/9+4
y=x^2/27+4/3=(x^2+36)/27
f^-1(x)=(x^2+36)/27
..
Checking radican:
3x-4≥0
3x≥4
x≥4/3
Domain of f: [4/3,∞)
Range of f: [0,∞)
..
Domain of f^-1: (0,∞)
Range of f^-1: [4/3,∞)
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