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# Exam3 4 - Betancourt Daniel – Exam 3 – Due May 1 2007...

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Unformatted text preview: Betancourt, Daniel – Exam 3 – Due: May 1 2007, 11:00 pm – Inst: Diane Radin keywords: optimization, cost, fence, rectangle, 004 (part 1 of 1) 10 points A function f is known to have an inverse f −1 . Which of the following could be the graph of y = f (x)? 5 4 1.3 2 1 0 -1 -2 -3 -4 -5 5 4 2.3 2 1 0 -1 -2 -3 -4 -5 5 4 3.3 2 1 0 -1 -2 -3 -4 -5 5 4 4.3 2 1 0 -1 -2 -3 -4 -5 2 2 4 −4 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 2 −4 −2 −2 2 4 5 4 4 3 2 2 1 0 -1 −4 −2 2 4 -2 −2 -3 -4 −4 -5 -5 -4 -3 -2 -1 0 1 2 3 4 5 keywords: 005 (part 1 of 1) 10 points −4 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 2 −4 −2 −2 2 4 -5 -4 -3 -2 -1 0 1 2 3 4 5 4 Determine the inverse function, f −1 , of f when √ f (x) = 3 x , (x ≥ 0) . 1. f −1 (x) = −4 correct 12 x, 3 1 2. f −1 (x) = − x2 , 3 (x ≤ 0) (x ≥ 0) 3. f −1 (x) does not exist 2 −4 −2 −2 −4 4 Explanation: If f has an inverse it must be a one-to-one function; equivalently, its graph must pass the horizontal line test. The only graph having this property is 4 −4 −2 −2 5 4 4 5.3 2 2 1 0 -1 −4 −2 24 -2 −2 -3 -4 −4 -5 -5 -4 -3 -2 -1 0 1 2 3 4 5 2 4 -5 -4 -3 -2 -1 0 1 2 3 4 5 4. f −1 (x) = 12 x 3 5. f −1 (x) = 12 x, 3 Explanation: (x ≥ 0) correct ...
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