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7.Let \\(f:A\\rightarrow B\\)\n , which reads ―f is a function of A onto B. The set A and B are called the…
a.range and image
b.codomain and domain
c.domain and codomain
d.domain and range
8.f \\(f:A\\rightarrow B\\) is___________________ if \\(f(a)= f(a^{\'})\\)\n implies \\(a=a^{\'}\\) or, equivalently, \\(a=a^{\'}\\)\nimplies f(a)=f(a^{\'})\n\n
a.injective functions
b.surjective functions
c.identity functions
d.constant function
a.range and image
b.codomain and domain
c.domain and codomain
d.domain and range
8.f \\(f:A\\rightarrow B\\) is___________________ if \\(f(a)= f(a^{\'})\\)\n implies \\(a=a^{\'}\\) or, equivalently, \\(a=a^{\'}\\)\nimplies f(a)=f(a^{\'})\n\n
a.injective functions
b.surjective functions
c.identity functions
d.constant function
4.Let the function \\( f:R\\rightarrow R\\) be defined by the formula \\(f(x)=x^{2} \\) . Then f \n\n
a.not a one-one function
b.a one-one function
c.identity function
d.constant function
5.Let f map \\(A\\) into \\(B\\). Then \\(f\\) is called a ______________ if different elements in \\(B\\) are assigned to different elements in \\(A\\)
a.constant function
b.surjective functions
c.injective functions
d.identity functions
6.If f and g are functions defined on the same domain D and if f (a) = g (a) for every \\(a\\in D\\), then the functions f and g are\n
a.surjective
b.injective
c.identical
d.equal
a.not a one-one function
b.a one-one function
c.identity function
d.constant function
5.Let f map \\(A\\) into \\(B\\). Then \\(f\\) is called a ______________ if different elements in \\(B\\) are assigned to different elements in \\(A\\)
a.constant function
b.surjective functions
c.injective functions
d.identity functions
6.If f and g are functions defined on the same domain D and if f (a) = g (a) for every \\(a\\in D\\), then the functions f and g are\n
a.surjective
b.injective
c.identical
d.equal
1.Let the function \\( f:R\\rightarrow R\\) be defined by the formula \\(f(x)=x^{2} \\) . Then the range of f consists of ______\n\n
a.the positive real numbers and one
b.the positive real numbers and zero
c.the negative real numbers and zero
d.the negative real numbers and one
2.Let f assign to each real number its square, that is, for every real number \\(x\\) let \\(f(x)=x^{2}\\)\n. The domain and co-domain of f are
a.both the real numbers
b.None of the option
c.both the rational numbers
d.both the natural numbers
3.Let \\(f(x)=x^{2}\\) where x is a real number. Let \\(g(x)=x^{2}\\)\n where x is a complex number. Which of the statement is true
a.the function f is not equal to g since they have different codomains
b.the function f is equal to g since they have different domains
c.the function f is equal to g since they have different codomains
d.the function f is not equal to g since they have different domains
a.the positive real numbers and one
b.the positive real numbers and zero
c.the negative real numbers and zero
d.the negative real numbers and one
2.Let f assign to each real number its square, that is, for every real number \\(x\\) let \\(f(x)=x^{2}\\)\n. The domain and co-domain of f are
a.both the real numbers
b.None of the option
c.both the rational numbers
d.both the natural numbers
3.Let \\(f(x)=x^{2}\\) where x is a real number. Let \\(g(x)=x^{2}\\)\n where x is a complex number. Which of the statement is true
a.the function f is not equal to g since they have different codomains
b.the function f is equal to g since they have different domains
c.the function f is equal to g since they have different codomains
d.the function f is not equal to g since they have different domains
Given the following production function; Y=AX^(3/4) X^(1/4)
Required:
Calculate the degree of homogeneity of the above function and comment
on the returns to scale.
Required:
Calculate the degree of homogeneity of the above function and comment
on the returns to scale.
Which of the following quantities is not an example of direct variation?
A. Nature of activity and heart beat
B. Speed and distance covered by a car in an hour
C. Hard work and success
D. Socio-economic status and number of friends
A. Nature of activity and heart beat
B. Speed and distance covered by a car in an hour
C. Hard work and success
D. Socio-economic status and number of friends
Marcus provides math tutoring lessons to ICON students. The amount of hours he is willing to tutor (supply) (Q) depends on the price he charges (P) in the following way: Q= 3P+2. The demand for his tutoring services is given by Q=5-2P.
If the tutor find a well paid part-time job, then
a) the supply curve will shift to the right
b) none of the above
c) the demand curve will shift to the right
d) the supply curve will shift to the left
e) the demand curve will shift to the left
If the tutor find a well paid part-time job, then
a) the supply curve will shift to the right
b) none of the above
c) the demand curve will shift to the right
d) the supply curve will shift to the left
e) the demand curve will shift to the left
With reference to the equation what do these points represent?
I. (5,273)
I. (5,273)
The sketch above shows graphs of the functions f and g. The graph of f is a parabola, with vertex B. The graph of g is a straight line which cuts the parabola at E on the y–axis and at A. The equation of f can be written as y =ax2 −x−6. The equation of g can be written as y =x+c. The line SR is parallel to the y-axis, where R is a point on the graph of f and S is a point on the graph of g. 7.1 (a) Show that a = 2. (b) Find the co-ordinates of B. (c) Find the co-ordinates of D. 7.2 (a) Find the equation of the straight line. (b) Find the co-ordinates of A. 7.3 Determine the maximum length of SR between E and A. 7.4 Use the graphs (i.e. do not solve an inequality) to determine all values of x for which
An aircraft flies into the north easterly direction at 750 km/h. There is a moderate Wind blowing at 5 km/h from west to east.
(i) Draw a vector diagram to represent the problem.
(ii) After travelling for two hours, find the distance travelled.
(i) Draw a vector diagram to represent the problem.
(ii) After travelling for two hours, find the distance travelled.
QUESTION 9
There are 2 blue pens, denoted as b1 and b2, 3 red pens, r1, r2 and r3, and 2 green pens, g1 and g2, in a closed box. Suppose you draw two pens together without first looking at the pens.
9.1 What is the sample space, S, in this case? (Give it as a set.) (4)
9.2 Determine n (S). (1)
9.3 Write down, as a set, the event E ” drawing a red and a green pen”. (2)
9.4 Determine n (E). (1)
9.5 What is the probability that you will draw a red and a green pen together? (2)
There are 2 blue pens, denoted as b1 and b2, 3 red pens, r1, r2 and r3, and 2 green pens, g1 and g2, in a closed box. Suppose you draw two pens together without first looking at the pens.
9.1 What is the sample space, S, in this case? (Give it as a set.) (4)
9.2 Determine n (S). (1)
9.3 Write down, as a set, the event E ” drawing a red and a green pen”. (2)
9.4 Determine n (E). (1)
9.5 What is the probability that you will draw a red and a green pen together? (2)
