Question 5: In diagram below, the function g maps set P to set Q and the function h maps set Q to set R. Find (a) in terms of x, the function (i) which maps set Q to set P, (ii) h(x). (b) the value of x such that gh(x) = 8x + 1. Solution: … Read more

Question 3: Given that f : x → hx + k and f2 : x → 4x + 15.   (a) Find the value of h and of k. (b) Take the value of h > 0, find the values of x for which f (x2 ) = 7x Solution: (a) Given f (x) = hx … Read more

Question 1: The function f and g is defined by f:x↦2x−3 g:x↦ 2 x ;x≠0 Find the expression for each of the following functions (a) ff, (b) gf, (c) f-1 , Calculate the value of x such that ff(x) = gf(x). Solution: (a) ff( x )=f[ f( x ) ]          =f( 2x−3 )          =2( 2x−3 … Read more

Question 5: It is given the functions g(x) = 3x and h(x) = m – nx, where m and n are constants. Express m in terms of n such that hg(1) = 4. Solution: hg( x )=h( 3x )  =m−n( 3x )  =m−3nx hg( 1 )=4 m−3n( 1 )=4 m−3n=4 m=4+3n Question 6: Given the … Read more

Question 1:Diagram below shows the relation between set M and set N in the graph form.State(a) the range of the relation,(b) the type of the relation between set M and set N.Solution: (a) Range of the relation = {p, r, s}.(b) Type of the relation between set M and set N is many to one relation. … Read more

Composite Function If function f : X ↦ Y , and function g : Y ↦ Z , hence, composite function g f : X ↦ Z Example: If, f : x ↦ 2 x + 5 and g : x ↦ x 2 − 1 , find g f ( 2 ) Answer: f … Read more

Example 1 Given the function f : x → 6 x + 1 . Find the value of p if f ( 4 ) = 4 p + 5 .Answer: f : x → 6 x + 1 f ( x ) = 6 x + 1 f ( 4 ) = 6 ( 4 … Read more

(B) Domain, Range, Objects and Images of a Function Example: The arrow diagram above represents the function f : x → 2×2 – 5. State (a) the domain, (b) the range, (c) the image of –2, (d) the objects of (i) –3, (ii) –5.   Solution: (a) Domain = {–2, –1, 0, 1, 2}. (b) … Read more

As shown in figure above, for a function f : X → Y , each element x in the domain X has a unique image y in the codomain Y.  The function can be written as: y = f ( x ) o r f : x ↦ f ( x ) For y = … Read more