Rolles Theorem - Calculus One - Solved Exam, Exams of Calculus

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Midterm 1 2 Question 1. (a) (5 points) Is the function f(a) =) even, odd or neither? Explain your reasoning. cos (x) cos (-x) = f (- x) fi=e 7 e since cos(x) =cos(-x) Fac 1s EVEN] (b) (5 points) Find the domain and range of the function below. (2) = In(a — 5) Domain =¢x: x-5>0F (5, 26) Range = (-08, 2) I {c) (5 points) Is the function g(x) = In(w — 5) one-to-one? If it is one-to-one, find a formula for the inverse of g(x). If it is not, explain why it is not a one-to-one function. In (x,-5) = |n (x, -5) tal a’, Inlxy-) ¢ 2 There fore X,-S = x,-5 es xX, =X, gf) is Formuda r the inverse ONE-TO-ONE f y ala (1-5) 9 X-S20" rrapease oF gle) SS xXme4ye Wa OrS,