73 and 75 Restricting the Domain In Exercises 7178 restrict

73 and 75

Restricting the Domain In Exercises 71-78, restrict the domain of the function f so that the function is one-to-one and has an inverse function. Then find the inverse function f-1. State the domains and ranges of f and f-1. Explain your results. (There are many correct ility to rizontalanswers.) function 73. f(x) = (x + 6)2 75, f(x) =-2t + 5 76, f(x) = 1x2-1 74, f(x) = (x-4 4l Inverse 77. x)-4+1 ) find the oth f and 78. f(x) =-1x-11-2 ate axes, Composition with Inverses In Exercises 79-84,

Solution

Ans: For inverse to exist the function must be one to one i.e, every element in range should correspond to exactly one element in the domain set.

73. Here the function\'s graph is exactly symmetrical about x = -6. So the domain for inverse to exist would be (-¤, -6) or (-6, ¤) as the function will be 1 to 1 in these ranges.

75. Here again the graph is symmetrical about y axis because of the x^2 term. Therefore the domain will be (-¤, 0) or (0, -¤) .

¤ denotes infinity.