Reference no: EM132361538

Mathematics Assignment -

Q1. For f(x) = 2x - 2 and g(x) = -x² + 1, find the composite function defined by (fog)(x).

a) -2x²

b) -4x² + 2x - 2

c) 4x² - 8x + 4

d) 2x² - 2

e) -2x² + 1

Q2. Solve: x/(x-4) ≤ 0  

a) (-∞, -0)Y(4, ∞)

b) [0, 4)

c) [0, 4]

d) (-∞, 0]Y(4, ∞)

e) (-∞, 0]Y[4, ∞)

Q3. Solve for x: log₃x + log₃(x+6) = 3

a) x = -3 only

b) x = 9 only

c) x = 3 and x = -9

d) x = 3 only

e) x = -3 and x = 9

Q4. The graph below represents a shift of the graph of y = lnx. Which of the following is the best choice for the graph's equation? [Hint: Try sketching the graph of y = lnx on the same axes below, to help you see the shift.]

a) y = ln(x-4)

b) y = ln(x-3)

c) y = ln(x+3)

d) y = ln(x) + 4

e) ln 4x

Q5. Solve for x: log₂1/(x+1) = -1

a) x = -1 only

b) x = 3 only

c) x = 1 only

d) x = -3 only

e) x = 1, 3

Q6. Find the x-intercepts and vertex for f(x) = 2x² + 4x - 30.

a. x-intercepts (-3, 0) and (-5,0); vertex (-2, -16)

b. x-intercepts (3, 0) and (5,0); vertex (-1, -32)

c. x-intercepts (3, 0) and (-5,0); vertex (-1, -32)

d. x-intercepts (3, 0) and (-5,0); vertex (-2, -16)

e. x-intercepts (-3,0) and (-5,0); vertex (-1, -32)

Q7. Solve for x: 3^2x-3 = 27^x-2

a) x = 3

b) x = -1

c) x = -3

d) x = -9

e) x = 1

Q8. Perform the operation and express your answer in simplest complex form. (3+5i)(2-i).

a) 11+7i

b) 6+7i-5i²

c) 1+7i

d) 11-7i

e) 1-7i

Q9. What are the center and radius of x² + y² - 2x + 6y = 3?

a) (1, -3), r = 13

b) (-1, 3), r = 13

c) (1, -3), r = √(13)

d) (-1, 3), r = √(13)

e) (1, -3), r = 1

Q10. Given the circle x² + y² = 169, what is the equation of the tangent line at the point (12, -5)?

a) -12x - 5y = -169

b) 12x + 5y = -169

c) -12x + 5y = -169

d) 5x + 12y = 169

e) -5x + 12y = 169

Q11. Simplify (2ab)⁵

a) 2a⁵b⁵

b) 32a⁵b⁵

c) a⁵b⁵

d) 10a⁵b⁵

e) 10ab

Q12. What is the minimum value of y = x² - 4x - 6?

a) 12

b) -2

c) 6

d) -10

e) -6

Q13. Find the domain of f(x) = √(3x -2)

a) {x|x is a real number and x = 2/3}

b) {x|x is a real number and x ≤ 3/2}

c) {x|x is a real number and x ≥ 3/2}

d) {x|x is a real number and x ≤ 2/3}

e) {x|x is a real number and x ≥ 2/3}

Q14. Given the function f(x) = x² + 3x + 4. What can you say about the graph's x-intercepts?

a) The graph has NO x-intercepts.

b) The graph has ONE RATIONAL x-intercept.

c) The graph has TWO RATIONAL x-intercepts.

d) The graph has TWO IRRATIONAL x-intercepts.

e) Not enough information is provided.

Q15. Which equation best represents the graph below?

a) y = x + 2

b) y = |x| + 2

c) y = |x+2|

d) y = |x|

e) y = x

Q16. Solve: x^-2 + x^-1 = 6.

a) x = - 1/3 or x = 1/2

b) x = - 2 or x = 3

c) x = 3 only

d) x = 1/3 only

e) x = 1/6 only

Q17. Given the function f(x) = x³ - 6, find f^-1(x).

a) f^-1(x) = x^1/3 + 6

b) f^-1(x) = (x^1/3+6)/6

c) f^-1(x) = (x+6)³

d) f^-1(x) = (x-6)³/6

e) f^-1(x) = (x+6)^1/3

Q18. Solve the system of equations: 2x² + y² = 24 and x² - y² = -12. How many real solutions are there to the system?

a) No solution

b) 1 solution

c) 2 solutions

d) 3 solutions

e) 4 solutions

Q19. Let f(x) = -(x - 3)² + 8. Find the vertex and determine if it is a maximum or minimum.

a) (-3, -8) max

b) (-3, -8) min

c) (3, 8) max

d) (3,8) min

e) (3, -8) max

Q20. Solve for x. √(2x-1) + 2 = x.

a) 5 only

b) 5 and 1 only

c) no solution

d) 1 only

e) 0 only

Q21. Write as a single logarithm. Assume that all variables represent positive real numbers.

3logx - logy + 2logz

a) log x³yz²

b) -log x³yz²

c) log x³/yz²

d) log x³z²/y

e) -6log x³yz²

Q22. Simplify √(27x⁹y³z⁵) (Assume that the variables do not have negative values.)

a) 27x⁴yz²√(xyz)

b) 3x⁴yz²√(3xyz)

c) 3x²yz²√(3x⁷y²z⁴)

d) 3x⁸y²z⁴√(3xyz)

e) 3x²yz²

Q23. Find the function f(x) that describes the line containing (2, 3) and (5, 15).

a) f(x) = 4x - 5

b) f(x) = 4x - 6

c) f(x) = 4x

d) f(x) = 2x - 3

e) f(x) = 5 - 4x

Q24. Solve: a = -2a² - 2.

a) ¼ ± ¼i

b) -¼ ± ¼i

c) 5/4, - 3/4

d) (-1±√(15))/4

e) (-1±√(17))/4

Q25. Rationalize the denominator. 9/(6+√3)

a) (6 - √3)/3

b) 3(6 - √3)

c) 3(6+√3)/13

d) 3(6+√3)/11

e) 3(6-√3)/11.