Pre Calculus 9th Edition Chapter 5 Review
Pre Calculus 9th Edition Chapter 5 Review
Pre Calculus 9th Edition Chapter 5 Review
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Date___________________________________
Chapter 5 Review
For the given functions f and g, find the requested composite function.
3
5
, g(x) =
;
Find (f g)(x).
1) f(x) =
x-5
2x
Answer:
6x
5 - 10x
1200 - 6p
+ 800
40
0, x
g.
-7}
2 - x; g(x) = 2x - 1
Answer: x| -
1
2
3
2
x+8
5
300.
x
+ 800. Assuming that all items produced are sold, find
20
Answer: C =
2
x + 200, 0
3
-5}; range of f: {y y
3}
Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of
the inverse.
8) f(x) = 3x + 4
4
,R= y y
3
0 ;
0 ,R= y y -
4
3
1
27
Answer:
12) f(x) = 2 (x - 2) + 2.
Answer:
Answer:
Answer: -
1
2
19) f(x) = ln
1
x+3
Answer: (-3, )
Graph the function.
20) f(x) = 2 - ln(x + 4)
Answer:
ln 7
5
The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake
x
according to this function M(x) = log
, where x 0 = 10-3 .
x0
23) What is the magnitude of an earthquake whose seismographic reading is 6.8 millimeters at a distance of 100
kilometers from its epicenter? Round the answer to the nearest tenth.
Answer: 3.8
Suppose that ln 2 = a and ln 5 = b. Use properties of logarithms to write each logarithm in terms of a and b.
4
24) ln 40
Answer:
1
(3a + b)
4
26) ln
5
8
2
logb x + logb y - logb z
3
3
3
(x + 9)(x - 3) 3/4
,
(x - 1)2
Answer:
x>3
3
3
3
ln (x + 9) + ln (x - 3) - ln (x - 1)
4
4
2
28) ln
m2 j1/3
b n3/5 k3
x2 - 3x - 4
x2 - 2x - 3
- ln
+ ln (x2 - 8x + 16), x > 0
x-3
x+9
Answer: ln
(x - 4)3(x + 9)
(x - 3)2
5
7
Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
32) ln x + ln (x + 7) = -4
Answer:
-7 +
49 + 4e-4
2
0.003
Answer: {7}
Solve the equation.
34) 3 52t - 1 = 75
Answer:
3
2
Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
35) 3 x = 41 - x
Answer:
ln 4
ln 3 + ln 4
0.558
44) The size P of a small herbivore population at time t (in years) obeys the function P(t) = 900e0.22t if they have
enough food and the predator population stays constant. After how many years will the population reach 3600?
Answer: 6.3 yrs