10Amidterm1_v2_ANS

# 10Amidterm1_v2_ANS - Name PID TA Sec No Sec Time Math10A...

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Unformatted text preview: Name : PID : TA : Sec. No : Sec. Time : Math10A Midterm 1. January 28 2011 Turn off and put away your cell phone. No calculators or any other electronic devices are allowed during this exam. You may use one page of notes, but no books or other assistance during the exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write all your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clarification. # Points Score 1 6 2 6 3 6 4 6 Σ 24 Problem 1 (6 points): Given f ( x ) = √ x- 2 , g ( x ) = x 2 + 9 , find each of the following: (a) The domain of f . f is defined only when x- 2 is nonnegative (that is, x ≥ 2). So the domain is [2 , ∞ ) (b) The range of f . Given the domain [2 , ∞ ), the possible outputs of f ( x ) are all nonnegative real numbers, so the range is [0 , ∞ ). (c) f (11) g (0) = ( √ 11- 2)(0 2 + 9) = (3)(9) = 27 . (d) f ( g (- 3)) = f ((- 3) 2 + 9)) = f (18) = √ 18- 2 = 4 . (e) g ( f ( x )) = ( √ x- 2) 2 + 9 = x- 2 + 9 = x + 7. (f) f- 1 (3) Find f- 1 ( x ) by solving for y in x = √ y- 2. So f- 1 ( x ) = x 2 + 2 (with domain [0 , ∞ )), and f- 1 (3) = 11 . Problem 2: A new radioactive material called mathium was discovered. Each year,A new radioactive material called mathium was discovered....
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10Amidterm1_v2_ANS - Name PID TA Sec No Sec Time Math10A...

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