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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0/8
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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0/2
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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0/2
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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0/2
(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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