StudentAidUnit 3: Sets and Functions — Exercise 3 3
9th Class Mathematics · Unit 3: Sets and Functions
3.3.1.For A = {1, 2, 3, 4}, find the following relations in A. State the domain and range of each relation. (i) {(x,y)|y=x} (ii) {(x,y)|y+x=5} (iii) {(x,y)|x+y<5} (iv) {(x,y)|x+y>5}
Result
(i)
{(1,1),(2,2),(3,3),(4,4)}; Domain={1,2,3,4}, Range={1,2,3,4}
(ii)
{(1,4),(2,3),(3,2),(4,1)}; Domain={1,2,3,4}, Range={1,2,3,4}
(iii)
{(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)}; Domain={1,2,3}, Range={1,2,3}
(iv)
{(2,4),(3,3),(3,4),(4,2),(4,3),(4,4)}; Domain={2,3,4}, Range={2,3,4}
3.3.2.Which of the following diagrams represent functions and of which type? [Fig (1): 1→a, 1→b, 2→c, 3→d; Fig (2): a→1, b→3, c→5; Fig (3): 1→a, 2→b, 3→c; Fig (4): l→x, m→x, m→y, n→z]
Result
Fig (1)
Not a function (1 maps to both a and b)
Fig (2)
A function; bijective
Fig (3)
A function; bijective
Fig (4)
A function; into
3.3.3.If g(x) = 3x + 2 and h(x) = x^2 + 1, then find: (i) g(0) (ii) g(-3) (iii) g(2/3) (iv) h(1) (v) h(-4) (vi) h(-1/2)
Working
(i)
g(0)=3(0)+2
Result
(i)
g(0)=2
Working
(ii)
g(-3)=3(-3)+2=-9+2
Result
(ii)
g(-3)=-7
Working
(iii)
gleft(23right)=3left(23right)+2=2+2
Result
(iii)
gleft(23right)=4
Working
(iv)
h(1)=(1)2+1=1+1
Result
(iv)
h(1)=2
Working
(v)
h(-4)=(-4)2+1=16+1
Result
(v)
h(-4)=17
Working
(vi)
hleft(-12right)=left(-12right)2+1=14+1
Result
(vi)
hleft(-12right)=54
3.3.4.Given that f(x) = ax + b + 1, where a and b are constant numbers. If f(3) = 8 and f(6) = 14, then find the values of a and b.
Working
f(3)=3a+b+1=8 ⇒ 3a+b=7 quad (i)
f(6)=6a+b+1=14 ⇒ 6a+b=13 quad (ii)
(ii)-(i): 3a=6 ⇒ a=2
Result
a=2, b=7-3(2)=1
3.3.5.Given that g(x) = ax + b + 5, where a and b are constant numbers. If g(-1) = 0 and g(2) = 10, find the values of a and b.
Working
g(-1)=-a+b+5=0 ⇒ -a+b=-5 quad (i)
g(2)=2a+b+5=10 ⇒ 2a+b=5 quad (ii)
(ii)-(i): 3a=10 ⇒ a=103
Result
b=5-2left(103right)=-53
3.3.6.Consider the function defined by f(x) = 5x + 2. If f(x) = 32, find the x value.
Working
5x+2=32
5x=30
Result
x=305=6
3.3.7.Consider the function f(x) = cx^2 + d, where c and d are constant numbers. If f(1) = 6 and f(-2) = 10, then find the values of c and d.
Working
f(1)=c+d=6 quad (i)
f(-2)=4c+d=10 quad (ii)
(ii)-(i): 3c=4 ⇒ c=43
Result
d=6-43=143