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Decide whether each function is one-to-one

Question : Decide whether each function is one-to-one : 2151604

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Decide whether each function is one-to-one.

1) (i) f(x) = x2 - 2

(ii)

A) (i) No; (ii) Yes

B) (i) No; (ii) No

C) (i) Yes; (ii) No

D) (i) Yes; (ii) Yes

Find f-1(x) for the one-to-one function f(x) shown.

2) f(x) = (3)Ö(x + 5)

A) f -1(x) = x3 - 5

B) f -1(x) = x2 + 5

C) f -1(x) = x3 + 5

D) f -1(x) = x2 - 5

Graph the inverse of f, given the graph of f below.

3)

v

A)

B)

C)

D)

Graph the function.

4) f(x) = 4x

A)

B)

C)

D)

5) g(x) = log4x

A)

B)

C)

D)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

6) Explain how the graph of the function g(x) = log6x can be obtained from the graph of the functionf(x) = 6x.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the equation. Give the exact solution.

7) 5x = (1/125)

A) {3}

B) {-3}

C) {(1/25)}

D) {(1/3)}

8) 16x = 32(2x + 2)

A) - (5/3)

B) - (1/3)

C) - 2

D) (5/3)

Solve the problem.

9) The growth in the population of a certain rodent at a dump site can be modeled by the exponential function A(t)= 461e0.016t, where t is the number of years since 1979. Estimate the population in the year 2000.

A) 323

B) 468

C) 655

D) 645

Write in logarithmic form.

10) 10-3 = 0.001

A) log3.10 = -3

B) log3-3 = .10

C) log100.001 = -3

D) log10-3 = 0.001

Write in exponential form.

11) log416 = 2

A) 42 = 16

B) 416 = 2

C) 24 = 16

D) 162 = 4

Solve the equation.

12) log1/5 x = -4

A) {(1/625)}

B) {625}

C) {(1/1,024)}

D) {1,024}

13) x = log255

A) {(1/2)}

B) {-2}

C) {- (1/2)}

D) {2}

14) logx25 = 2

A) 2

B) 2 or -2

C) 5

D) 5 or -5

Fill in the blanks with the correct responses.

15) The value of log28 is __________. This means that if we raise ____ to the power ____, the result is ____.

A) 32 = 8

B) 3; 2; 3; 8

C) 83 = 2

D) 28 = 3

Use properties of logarithms to write each expression as a sum or difference of logarithms. Assume that variables represent positive real numbers.

16) log4xy2

A) log4x + 2log4y

B) 2log2x - 2log2y

C) 2log4x - log4y

D) log2x + log2y

17) log5(9)Ö(13)/s2r)

A) log513 - log5s - log5r

B) (1/9)log513 - 2log5s - 2log5r

C) (1/9)log513 - 2log5s - log5r

D) 9log513 - 2 log5s - log57

Use properties of logarithms to write each expression as a single logarithm. Assume that variables represent positive real numbers, with base ≠ 1.

18) 3logax - logay

A) loga(x3/y )

B) loga(3x/y)

C) loga(x3 - y)

D) logax3 ÷ logay

19) 4logat - (4/5)logas + (1/2)logav - 6logau

A) loga (t4u6/v1/2s4/5)

B) loga (t4v1/2/s4/5u6)

C) loga (t4s4/5/v1/2u6)

D) loga (4t - (4/5)s + (1/2)v - 6u)

Find the logarithm. Give an approximation to four decimal places.

20) log2.48

A) 0.3,766

B) 0.4,116

C) 0.3,945

D) 0.9,083

21) ln0.984

A) 0.0161

B) 0.0070

C) -0.0161

D) -0.0070

Use the change-of-base rule to express the given logarithm in terms of common logarithms, in terms of natural logarithms, and correct to four decimal places.

22) log2325.88

log23

A) (log25.88/log10); (ln25.88/ln10); 1.4130

B) (log25.88/log23); (ln25.88/ln23); 1.0376

C) (25.88/23); 1.1252

D) (log23/log25.88); (ln23/ln25.88); 0.9637

Solve, giving the correct solution to four decimal places.

23) 17x = 26

A) {1.5294}

B) {1.4249}

C) {0.8700}

D) {1.1500}

Solve the equation.

24) log2(x - 4) + log2(x - 10) = 4

A) x = 2

B) x = 13

C) x = 12, x = 2

D) x = 12

Solve the problem.

25) Find the amount of money in an account after 6 years if $4,800 is deposited at 5% annual interest compounded quarterly. Assume no money is withdrawn.

A) $6,475.29

B) $6,455.47

C) $6,432.46

D) $6,467.29

26) Suppose $8,000 is invested at 7.25% annual interest, compounded continually. (i) What will be the amount in the account in 9 years if no money is withdrawn? (ii) How long will it take for the initial principal to double? Round to the nearest tenth of a year.

A) (i) $15,362.69; (ii) 9.6 years

B) $8,000.00; (ii) 12.6 years

C) $7,458.36; (ii) 5.6 years

D) $8,601.54; (ii) 15.2 years

Solution
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