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 onetoone
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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 Spring '08
 CLARK,C.W./HOY,R.R
 Inverse function, Injective function, 3, Betancourt, Diane Radin

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