The onetoone function f is defined below fx Squareroot3x 9

The one-to-one function f is defined below. f(x) = Squareroot3x + 9 Find f^-1 the inverse of f Then give the domain of f^-1 using interval notation.

Solution

Let y = f(x). Then y = ( 3x+9) so that y² = 3x + 9 or, 3x = y² -9 and x =( 1/3)(y² -9). Now, on interchanging x and y , we have y = (1/3)(x² -9). Thus the inverse function is f(x) = (1/3)(x² -9).The domain of f^-1is R, the set of all real numbers. In interval notation, the domain of f^-1is ( - , + ).