Q10. Solve the equation log 4 (x + 2) = -1 a. {-7} b. {-7/4} c. {9/4} d. {9} Q12

Question

Q10. Solve the equation log 4 (x + 2) = -1
   a. {-7}
   b. {-7/4}
   c. {9/4}
   d. {9}

Q12. Find the inverse of the function and state its domain and range.
{(-3, 4), (-1, 5), (0, 2), (2, 6), (5, 7)}
   a. {(3, 4), (1, 5), (0, 2), (-2, 6), (-5, 7)}; D = {3, 1, 0, -2, -5}; R = {2, 4, 5, 6, 7}
   b. {(-3, -4), (-1, -5), (0, -2), (2, -6), (5, -7)}; D = {-3, -1, 0, 2, 5}; R = {-7, -6, -5, -4, -2}
   c. {(4, -3), (5, -1), (2, 0), (6, 2), (7, 5)} D = {2, 4, 5, 6, 7}; R = {-3, -1, 0, 2, 5}
   d. {(3, -4), (1, -5), (0, -2), (-2, -6), (-5, -7)}; D = {3, 1, 0, -2, -5}; R = {-7, -6, -5, -4, -2}

Q13. Find the domain of the composite function f g if f(x) = 28/x and g(x) = -8/(x - 7).
   a. {x | x 7}
   b. {x | x 0, x 7, x 4}
   c. {x | x 7, x 0}
   d. {x | x is any real number}

Q14. Express 6log b m - log b n as a single logarithm.
   a. log b m6 ÷ log b n
   b. log b (m6 - n)
   c. log b (m6/n)
   d. log b (6m/n)

Q15. In 1990, the population of a country was estimated at 4 million. For any subsequent year the population, P(t) (in millions), can be modeled by the equation P(t) = 240/(5 + 54.99e-0.0208t), where t is the number of years since 1990. Estimate the year when the population will be 21 million.
   a. approximately the year 2093
   b. approximately the year 2041
   c. approximately the year 2088
   d. approximately the year 2016

Q16. If 5x = 6,what does 5-2x equal?
   a. 1/36
   b. 36
   c. 1/12
   d. -36

Q17. For the functions f(x) = x2 + 4 and g(x) = x2 + 1, find the composite function (f g)(x).
   a. x4 + 5
   b. x4 + 17
   c. x4 + 2x2 + 5
   d. x4 + 8x2 + 17

Q18. A size 6 dress in Country C is size 52 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x) = 2(x + 20). Find a formula for the inverse of the function described.
   a. f -1(x) = (x - 20)/2
   b. f -1(x) = x - 20
   c. f -1(x) = (x/2) - 20
   d. f -1(x) = (x/2) + 20

Q19. If f(x) = 4x and g(x) = 12, find the point of intersection of the graphs of f and g by solving f(x) = g(x). Give an exact answer.
   a. (log 4 12, 12)
   b. (log 4 12, 4)
   c. (log 4 12, 0)
   d. (12, 12)

Q20. Find functions f and g so that f g = H(x) = (5 - 2x3)2.
   a. f(x) = 5 - 2x3 ; g(x) = x2
   b. f(x) = (5 - 2x)3 ; g(x) = x2
   c. f(x) = x2 ; g(x) = 5 - 2x3
   d. f(x) = x3 ; g(x) = (5 - 2x)2

Explanation / Answer

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Question 10)

Given

log4 (x+2) = -1

=>

(x+2) = 4^(-1)

x+2 = 1/4

x = 1/4 - 2

x = -7/4

Solution

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