Idea Solution
Solve the two sided inequality and show the solution on real line7 < 12x ≤ 10Step 1: subtract 1 from both sides and we get6<2x<9Step2: divide by 2 on both sides and we get3>x>5(note: symbols are reversed with a negative operation)So x can have a value between 3 and or equal to 5



0
5 4 3 2 1
Question 2; Marks: 10
Given two functions as:f(x) =
2
1
x x
− −
and g(x) =3
x
Find fog(x) also find the domain of
f
,
g
and
fogSolution:
Fog(x)=f(g(x))fog(x)=(g(x))
2
(g(x))1fog(x)=(3/x)
2
(3/x)1fog(x)=(9/x
2
)3/x1fog(x)= (x
2
3x+9)/x
2
(note: domain and ranges are to be found out yourselves, listen to lecture No. 6 for this)
Question 3; Marks:10
Simplify, then apply the rules of limit to evaluate
3 232
56lim9
x
x x x x
→
− +−
Solution:
Lim(x>3) x(x
2
5x+6) / x
2
3
2
Lim(x>3) x(x
2
3x2x+6) / (x3)(x+3)Lim(x>3) x(x(x3)2(x3)) / (x3)(x+3)Lim(x>3) x((x3)(x2)) / (x3)(x+3)Lim(x>3) x(x2) /(x+3) Now applying limits lim x>3=3(32)/3+3=3(1)/6=3/6=½