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Easy questions. No need for an explanation. only answers assignment_10__2.7_.pdfassignment_11__2.8_.pdf2/11/2016
Find
Assignment 10 (2.7)
f
(x).
g
√25−x2x+2
Find the domain of
f
g
(−2,5]
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Assignment 10 (2.7)
2. –/8 pointsSPreCalc7 2.7.015.
Consider the following functions.
9
,
x
Find (f + g)(x).
f(x) =
g(x) =
11
x + 11
Find the domain of (f + g)(x). (Enter your answer using interval notation.)
Find (f − g)(x).
Find the domain of (f − g)(x). (Enter your answer using interval notation.)
Find (fg)(x).
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Find
Assignment 10 (2.7)
f
(x).
g
Find the domain of
f
g
3. –/2 pointsSPreCalc7 2.7.028.MI.
Use f(x) = 3x − 4 and g(x) = 5 − x2 to evaluate the expression.
(a)
f(f(2))
(b)
g(g(3))
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Assignment 10 (2.7)
4. –/2 pointsSPreCalc7 2.7.029.MI.
Use f(x) = 2x − 4 and g(x) = 5 − x2 to evaluate the expression.
(a)
(f
g)(−2)
(b)
(g
f)(−2)
5. –/1 pointsSPreCalc7 2.7.033.MI.
Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the
gridlines.)
f(g(0)) =
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Assignment 10 (2.7)
6. –/1 pointsSPreCalc7 2.7.036.MI.
Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the
gridlines.)
(f
g)(−2) =
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Assignment 10 (2.7)
7. –/8 pointsSPreCalc7 2.7.049.MI.
Consider the following functions.
f(x) = x2,
Find (f
g(x) = x + 1
g)(x).
Find the domain of (f
Find (g
f)(x).
Find the domain of (g
Find (f
f)(x).
Find the domain of (f
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Find (g
Assignment 10 (2.7)
g)(x).
Find the domain of (g
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Assignment 10 (2.7)
8. –/8 pointsSPreCalc7 2.7.055.MI.
Consider the following functions.
x
,
x+8
g)(x).
f(x) =
Find (f
Find the domain of (f
Find (g
f)(x).
Find the domain of (g
Find (f
g(x) = 3x − 8
f)(x).
Find the domain of (f
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Assignment 10 (2.7)
Find (g
g)(x).
Find the domain of (g
9. –/1 pointsSPreCalc7 2.7.059.
Find f
g
h.
f(x) = x − 2,
g(x) =
x,
h(x) = x − 2
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2/11/2016
Assignment 10 (2.7)
10.–/1 pointsSPreCalc7 2.7.063.
Express the function F in the form f g. (Enter your answers as a comma­separated list. Use non­
identity functions for f(x) and g(x).)
F(x) = (x − 7)8
(f(x), g(x)) =
11.–/1 pointsSPreCalc7 2.7.066.
Express the function G in the form f
g. (There is more than one correct answer. The function is
of the form y = f(g(x)). Use non­identity functions for f(x) and g(x).)
G(x) =
1
x+9
(f(x), g(x)) =
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Assignment 10 (2.7)
12.–/4 pointsSPreCalc7 2.7.077.
A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 60 cm/s.
(a) Find a function g that models the radius as a function of time t, in seconds.
g(t) =
(b) Find a function f that models the area of the circle as a function of the radius r, in cm.
f(r) =
(c) Find f
f
g.
g=
What does this function represent?
This function represents the area of the ripple as a function of the radius.
This function represents time as a function of the area of the ripple.
This function represents the radius of the ripple as a function of time.
This function represents the radius of the ripple as a function of area.
This function represents the area of the ripple as a function of time.
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Assignment 10 (2.7)
13.–/1 pointsSPreCalc7 2.7.079.
A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of
9 cm/s. Express the surface area of the balloon as a function of time t (in seconds). (Let S(0) =
0.)
S(t) =
cm2
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Assignment 11 (2.8)
2. –/1 pointsSPreCalc7 2.8.009.
A graph of a function f is given.
Determine whether f is one­to­one.
Yes, f is one­to­one.
No, f is not one­to­one.
3. –/1 pointsSPreCalc7 2.8.013.
Determine whether the function is one­to­one.
f(x) = −7x + 4
is one­to­one
is not one­to­one
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Assignment 11 (2.8)
4. –/1 pointsSPreCalc7 2.8.017.
Determine whether the function is one­to­one.
h(x) = x2 − 5x
is one­to­one
is not one­to­one
5. –/2 pointsSPreCalc7 2.8.026.MI.
Assume that f is a one­to­one function.
(a) If f(5) = 15, find f −1(15).
f −1(15) =
(b) If f −1(30) = 15, find f(15).
f(15) =
6. –/1 pointsSPreCalc7 2.8.037.
Use the Inverse Function Property to determine whether f and g are inverses of each other.
f(x) = x − 9;
g(x) = x + 9
f and g are inverses of each other.
f and g are not inverses of each other.
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Assignment 11 (2.8)
7. –/1 pointsSPreCalc7 2.8.045.
Use the Inverse Function Property to determine whether f and g are inverses of each other.
1
1
, x ≠ 10; g(x) =
+ 10
x − 10
x
f and g are inverses of each other.
f(x) =
f and g are not inverses of each other.
8. –/1 pointsSPreCalc7 2.8.052.
Find the inverse function of f.
f(x) = 2×3 + 4
f −1(x) =
9. –/1 pointsSPreCalc7 2.8.055.
Find the inverse function of f.
f(x) =
x
x+5
f −1(x) =
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Assignment 11 (2.8)
10.–/1 pointsSPreCalc7 2.8.067.MI.
Find the inverse function of f.
f(x) =
3 + 8x
f −1(x) =
,
x≥0
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Assignment 11 (2.8)
11.–/2 pointsSPreCalc7 2.8.086.
The given function is not one­to­one.
g(x) = (x − 4)2
Restrict its domain so that the resulting function is one­to­one.
[3, ∞)
(−∞, 5]
(−∞, ∞)
[4, ∞)
(−5, ∞)
Find the inverse of the function with the restricted domain above.
g−1(x) =
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Assignment 11 (2.8)
12.–/1 pointsSPreCalc7 2.8.089.
Use the graph of f to sketch the graph of f −1.
Graph f −1 using closed endpoints for each segment.
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Assignment 11 (2.8)
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Assignment 11 (2.8)
13.–/5 pointsSPreCalc7 2.8.094.MI.
For his services, a private investigator requires a \$550 retainer fee plus \$80 per hour. Let x
represent the number of hours the investigator spends working on a case.
(a) Find a function f that models the investigator’s fee as a function of x.
f(x) =
(b) Find f −1.
f −1(x) =
What does f −1 represent?
f −1 represents the amount in dollars paid for x numbers of hours of investigation.
f −1 represents the amount in dollars paid beyond the retention fee for x numbers of
hours of investigation.
f −1 represents the number of hours of investigation the investigator spends on a
case for x dollars.
f −1 represents the maximum number of hours of investigation the investigator will
spend on a case.
f −1 represents the amount paid per each hour of investigation.
(c) Find f −1(1270).
f −1(1270) =
f −1(1270) represents the amount in dollars paid for 1270 hours of investigation.
f −1(1270) represents the amount in dollars paid beyond the retention fee for 1270
hours of investigation.
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Assignment 11 (2.8)
f −1(1270) represents the number of hours of investigation the investigator spends
on a case for \$1270.
f −1(1270) represents the maximum number of hours of investigation the
investigator will spend on a case.
f −1(1270) represents the amount paid per each hour of investigation.
14.–/1 pointsSPreCalc7 2.8.507.XP.
Find the inverse function of f.
f(x) =
9x − 1
x−2
f −1(x) =
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1.
-/1 points SPreCalc7 2.8.007.
My Notes
A graph of a function fis given.
y
х
0
Determine whether fis one-to-one.
Yes, f is one-to-one.
No, f is not one-to-one.
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