Page 196 - DMTH201_Basic Mathematics-1

Unit 6: Functions

8. The quotient of two odd function is ………… Notes
9. If f(x) is real valued function of a real variable then f is odd function if ………… equation
holds.

10. The Composition of an even function and an odd function is …………

6.9 Review Questions

1. Which of the following are exponential functions?
(a) f(x) = 3e- 2 x
(b) g(x) = 2 x/2

(c) h(x) = x 3/2
(d) g(x) = 15/7 x
x
2. What is the domain of an exponential function f(x) = kb ? What is the range? Describe the
shape of the graph for b > 1, and for b < 1. What happens to f(x) in each case when x becomes
very large (increases without bound) and as x becomes very small (decreases without
bound)? Are there any horizontal asymptotes?
3. Solve the following equations. You should not need to use logarithms for the first three.
x
(a) 2 = 32
x
(b) 5 = 1/125
2x
(c) (1/3) = 243
(d) 45 = 5 3x
(e) 500 = 1000e- .75 x

(f) 56 = 14(1 + e .195 x )
4. The population of bacteria in a culture is growing exponentially. At 12:00 there were 80
bacteria present and by 4:00 PM there were 500 bacteria. Find an exponential function f(t)
at
= ke that models this growth, and use it to predict the size of the population at 8:00 PM.
5. The last nuclear test explosion was carried out by the French on an island in the south
Pacific in 1996. Immediately after the explosion, the level of strontium-90 on the island
was 100 times the level considered to be “safe” for human habitation. If the half-life of
Strontium-90 is 28 years, how long will it take for the island to once again be habitable?
6. Which of the following functions are onto function if f : R R
(a) f(x) = 115x + 49
(b) f(x) = |x|
7. Which of the following functions are one-to-one functions?

(a) f : {20,21,22} {40,42,44} defined as f(x) = 2x
(b) f : {7,8,9} {10} defined as f(x) = 10
(c) f : I R defined as f(x) = x 3

(d) f : R R defined as f(x) = 2 + x 4
2
(e) f : N N defined as f(x) = x + 2x

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