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Unformatted text preview: } . (a) Show that the relation R has an inverse R-1 . (b) Find the equation for the inverse function f ( x ) given by R-1 and compute f (0) . 7. Let f ( x ) = ( x + 1) 2 + 1 and g ( x ) = x 2 . (a) Find the composition h ( x ) = g-1 ◦ f-1 ( x ) . (b) What is the domain of h ( x )? 8. Let z = 1 2 + 3 2 i . (a) Find z and show that z z = 1 . (b) If w = 1-i , ﬁnd in simplest x + i y form the ratio ξ = z w . 9. (a) Solve for x and check: 3 x-10 · 3-x =-9 . (b) After 4 years, 12 grams of a certain element decays to half of its original amount. If the equation A ( t ) = Pe kt can be used to the model the rate of decay, ﬁnd the value of the decay constant k. Show all work. 10. (a) Solve for x : 1 2 ln(2 x )-ln(3 x ) = 0 . (b) Let h ( x ) = ln( e x 2 +1 + 1) + 1 . Find two functions f ( x ) and g ( x ) such that h ( x ) = f ◦ g ( x ) . What are the domains of f ( x ) and g ( x ) , respectively?...
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- Fall '08
- Quadratic equation, Elementary algebra, Final Exam Answer