EXAM GUIDE *ELECTIVE* *MATHEMATICS FURTHER

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Examinable Questions

Q1(c)if f(x) =2x²+x/2and g(x)=1/x+4 Find:
(I)f(½),
(ii)f(¼) × g(½).

2(a) Under mapping h(x)=px² - qx +2.the image of 3 is 14 and the image of -2 is 24.
Find:
(I)The value of p and q
(ii)The elements whose image is 4

3.The function f and g are given as f(x)=x+3/x and g(x)=2+1.
Evaluate:(I)g(-2),(ii)f(-½).
The function f and g are defined as f:×->×-2 and g(×)->2ײ-1. Solve:
(I)f(×)=g(-½)
(ii) f(×)+g(×)=0.

4.Given that f(x)=2×-1 and g(×)=ײ +1:
(I)Find f(1+×):
(ii)Find the range of values of x for which f(x)<-3;
(iii)Simplify f(×)-g(×).

5. The function f and g are defined as
f:×->3×-2, g(×)=1/× (x≠0).
Evaluate: (i)f(-2).(ii)g(½).
Solve
(iii)f(x)=g(½),
(iv)f(x)=4×-2,

6.if f(x)=4x-2, find:
(I)f(2),
(ii)f(2t).
(b) if p=(3) and q=(-1) 2 3
I,find the vector representing
3p-q
ii,Given that:ap+bq3)

7.(a)if f(x)=2ײ-3x+4,Simplify
f(×)+3× .
(b)if g(x)=(×+3)(×-4)/2.
I,Find the values of x for which g(×)=0.
ii,Evaluate g(-1).
iii,Find the value of C for which g(c)=-3.

8.Two functions ,f and g are defined by
f:x- >2x²-1and g:x->3x+2
Where x is a real number.
I,if f(x-1)-7=0;
ii,Evaluate f(½)g(3)/f(4)-g(5)
(b)An operation (*) is defined on the set R of real numbers by m(*)n =n=-n/m²+1,
Where m,n€R.
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