Find domain, codomain and range of the following function.
(¡) A={-2,3,4}
F:A—>R such that F(x)=x³-2
(¡¡) A={-1,0,1,3,4}
g:A—>Z such that g(x)=2x-1
(¡¡¡) A:{X:x is a pri number <8}
h:A—>N such that h(x)=(x²+1)-x
Answers
Answer:
(i) domain = A
codomain = R ,(set of all real numbers)
range = {-10,25,62}
(ii) domain= A
codomain = Z ,(set of all integers)
range = {-3,-1,1,5,7}
(iii) domain = A
codomain = N ,(set of all natural numbers)
range = {3,7,21,43}
Step-by-step explanation:
Domain of a function is the set from which we are defining the function,
hence (i) domain of F is the set A={-2,3,4}.
(ii) domain of g is the set A= {-1,0,1,3,4}
(iii) domain of h is the set A = {x:x is a prime number<8}
= {2,3,5,7}
Codomain of a function is the set into which we are defining the function.
Hence (i) codomain of F is the set R
(ii) codomain of g is the set Z
(iii) codomain of h is the set N
Range of a function is the subset of the codomain which contains only the image elements. Therefore,
(i) range of F = {-10,25,62}
(putting the values -2,3,4 for x , and apply it in the equation of F(x))
when x=-2, F(-2)=2³-2 = (-2)³-2= -8-2=-10
when x=3, F(3)=3³-2 = 27-2 = 25
when x=4, F(4)=4³-2 = 64-2 = 62
(ii) range of g = {-3,-1,1,5,7}
(putting the values -1,0,1,3,4 for x , and apply it in the equation of g(x))
when x=-1, g(-1)=2(-1)-1 = -2-1 =-3
when x=0, g(0)=2(0)-1 = 0-1 = -1
when x=1, g(1)=2(1)-1 = 2-1 = 1
when x=3, g(3)=2(3)-1 = 6-1 =5
when x=4, g(4)=2(4)-1 = 8-1 =7
(iii) range of h = {3,7,21,43}
(putting the values 2,3,5,7 for x , and apply it in the equation of h(x))
when x=2, h(2)=(2²+1)-2 = 5-2=3
when x=3, h(3)=(3²+1)-3 = 10-3=7
when x=5 h(5)=(5²+1)-5 = 26-5=21
when x=7 h(7)=(7²+1)-7 = 50-7=43
hence the answers
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