The function fxis onetoone a Find its inverse and check your

The function f(x)is one-to-one (a) Find its inverse and check your answer. (b) Find the domain and the range off andf (a) f-1 (x) = (Simplify your answer.) (b) Find the domain off. Select the correct choice below and, if necessary, fill in the answer box to complete your choice 0 A. O B. ° C. The domain is(x(x2 9x-1 The domain is (xlxs Type integers or fractions. Use a comma to separate answers as needed.) The domain is {x Type integers or fractions. Use a comma to separate answers as needed) Type integers or fractions. Use a comma to separate answers as needed) D. The domain is the set of all real numbers Find the range off. Select the correct choice below and, if necessary, fill in the answer box to complete your choice 0 A. The range is {ylys B. The range is (yly2 O C. The 0 D. The range is the set of all real numbers Now, find the domain off Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A. The domain is(X1X2 O B. The domain is {x/ C. Type integers or fractions. Use a comma to separate answers as needed.) Type integers or fractions. Use a comma to separate answers as needed) Type integers or fractions. Use a comma to separate answers as needed.) The domain is xxa Type integers or fractions. Use a comma to separate answers as needed.) Type integers or fractions. Use a comma to separate answers as needed) The domain is xlxA Type integers or fractions. Use a comma to separate answers as needed.) D. The domain is the set of all real numbers

Solution

y = f(x) = 7x/(9x-1) or, (9x -1)y = 7x or, 9xy- y = 7x or, x(9y -7) = y so that x = y/(9y – 7). Now, on switching the places of x and y, we have f^-1(x ) = x/(9x -7).

The domain of f(x) is { x R: x 1/9} . Answer B is correct with 1/9 in the blank space.

The range of f is { y: y R, y 7/9}. Answer C is correct with 7/9 in the blank space.

The domain of f^-1(x) is{ x R: x 7/9} Answer C is correct with 7/9 in the blank space.

The range of f^-1(x) is { y: y R, y 1/9}. Answer C is correct, with 1/9 filling the blank space.