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Question 64620: Find the inverse of this function, and state the domain and range of both the original function and the inverse: F(x) = sqrt(2x-3)
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Find the inverse of this function, and state the domain and range of both the original function and the inverse: F(x) = sqrt(2x-3)
F(X)= SQRT(2X-3)......2X-3>=0 AS OTHERWISE , ITS SQUARE ROOT IS IMAGINARY.
HENCE DOMAIN IS 2X-3>=0.....2X>=3.........X>=3/2=1.5......[1.5,INFINITY)
SINCE , IN GENERAL IN MATHS WE TAKE ONLY THE POSITIVE VALUES OF SQRT...RANGE IS>=0...........[0,INFINITY)
INVERSE
Y =SQRT(2X-3)
Y^2=X-3
X=Y^2+3
HENCE INVERSE FUNCTION IS X^2+3
DOMAIN IS ALL REAL NUMBERS......[-INFINITY,+INFINITY)
RANGE IS >=3 SINCE MINIMUM VALUE OF X^2+3 IS 3 .....[3,INFINITY)
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