# SOLUTION: 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)

Algebra ->  -> SOLUTION: 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)      Log On

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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)