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The graph of the function is given in blue. Use transformations to create the function whose graph is shown in red.
y = sqrt(2 x - x^2)
y =
1
Maple Generated Plot Maple Generated Plot

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5. –/8 points Notes Question: SCalcET6M 1.3.029.
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0/8

Find each of the following functions and state their domains.
f(x) = x3 + 3x2
g(x) = 5x2 - 2
(a) f + g =
1

2
reals (0, infinity) x -3 x != +/-sqrt(2/5)

(b) f - g =
3

4
reals (0, infinity) x -3 x != +/-sqrt(2/5)

(c) fg =
5

6
reals (0, infinity) x -3 x != +/-sqrt(2/5)

(d) f/g =
7

8
reals (0, infinity) x -3 x != +/-sqrt(2/5)

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6. –/8 points Notes Question: SCalcET6M 1.3.031.
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0/5 0/5 0/5 0/5 0/5 0/5 0/5 0/5
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0/8

Find each of the following functions and their domains.
f(x) = x2 - 5
g(x) = 2x - 1
(a) f compose g =
1

2
x > 2 x 5 (-infinity, 1] (-infinity, infinity)

(b) g compose f =
3

4
x 5 x > 2 (-infinity, infinity) (-infinity, 1]

(c) f compose f =
5

6
(-infinity, 1] (-infinity, infinity) x 5 x > 2

(d) g compose g =
7

8
(-infinity, infinity) (-infinity, 1] x > 2 x 5

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7. –/8 points Notes Question: SCalcET6M 1.3.033.
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0/8

Find each of the following functions and their domains.
f(x) = 4 - 4x
g(x) = cos(x)
(a) f compose g =
1

2
x > 4 (-infinity, 4] x 0 (-infinity, infinity)


(b) g compose f =
3

4
(-infinity, 4] x > 4 (-infinity, infinity) x 0


(c) f compose f =
5

6
(-infinity, 4] x 0 x > 4 (-infinity, infinity)


(d) g compose g =
7

8
x 0 (-infinity, infinity) (-infinity, 4] x > 4

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8. –/8 points Notes Question: SCalcET6M 1.3.036.
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0/8

Find each of the following functions and their domains.
f(x) = x/(7 + x)
g(x) = sin(3 x)
(a) f compose g =
1

2
x != -7 text( and ) x != -49/8 R x != -7 \(-1, 1\)

(b) g compose f =
3

4
R x != -7 x != -7 text( and ) x != -49/8 \(-1, 1\)

(c) f compose f =
5

6
x != -7 x != -7 text( and ) x != -49/8 R \(-1, 1\)

(d) g compose g =
7

8
R x != -7 text( and ) x != -49/8 x != -7 \(-1, 1\)

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9. 0/1 points All Submissions Notes Question: SCalcET6M 1.3.039.MI.
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0/1

Find f compose g compose h.
f(x) = √x − 1
g(x) = x2
h(x) = x3 + 3
1
Your answer was incorrect, but has changed from what was graded.


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10. –/2 points Notes Question: SCalcET6M 1.3.042.
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0/1 0/1
0/5 0/5
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0/2

Express the function in the form f compose g. (Use only elementary functions, but not the identity function, g(x) = x.)
F(x) = csc(√x)
f(x) =
1

g(x) =
2

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11. –/2 points Notes Question: SCalcET6M 1.3.045.
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0/5 0/5
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0/2

Express the function in the form f compose g. (Use only elementary functions, but not the identity function, g(x) = x.)
u(t) = sqrt(cos(t)
f (t) =
1

g(t) =
2

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12. –/3 points Notes Question: SCalcET6M 1.3.048.
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0/3

Express the function in the form f compose g compose h. (Use only elementary functions, but not the identity function, g(x) = x.)
H(x) = root9(1 + abs(x))
f(x) =
1

g(x) =
2

h(x) =
3

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13. –/6 points Notes Question: SCalcET6M 1.3.051.
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0/6

Use the given graphs of f and g to evaluate each expression, or if the expression is undefined, enter UNDEFINED.
(a) f(g(2)) = 1

(b) g(f(0)) = 2

(c) (f compose g)(0) = 3

(d) (g compose f)(6) = 4

(e) (g compose g)(-2) = 5

(f) (f compose f)(4) = 6


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14. –/2 points Notes Question: SCalcET6M 1.3.061.
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0/5 0/5
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0/2

(a) If g(x) = 3x + 2 and h(x) = 9x2 + 12x + 9, find a function f such that f compose g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)
f =
1


(b) If f(x) = 4x + 9 and h(x) = 4x2 + 4x + 5, find a function g such that f compose g = h.
g(x) =
2

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15. –/4 points Notes Question: SCalcET6M 1.3.063.
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0/4

(a) Suppose f and g are even functions.
(i) f + g is 1.
(ii) fg is 2.

(b) What if f and g are both odd?
(i) f + g is 3.
(ii) fg is 4.

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