Functions

Question 6 (SPM 2018 – 8 marks):It is given that g : x → 2x – 3 and h : x → 1 – 3x.(a) Find(i) h (5)(ii) the value of k if  g( k+2 )= 1 7 h( 5 ), (iii) hg(x).(b) Hence, sketch the graph of y = | hg(x) | for –1 … 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 11 (SPM 2017 – 3 marks):Diagram 5 shows the graph of the function f : x → |1 – 2x| for the domain –2 ≤ x ≤ 4.Diagram 5 State(a) the object of 7,(b) the image of 3,(c) the domain of 0 ≤ f(x) ≤ 5.Solution:(a)The object of 7 is 4.(b)f (x) = |1 … 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

Example 4:(a) If f : x → x – 2, find f -1 (5), (b) if f:x→ x+9 x−5 , x≠5, find  f −1 (3). Solution:   (a) f (x) = x– 2 Let y = f -1 (5) f (y) = 5 y – 2 = 5 y = 7 therefore, f -1 (5) = 7 (b) f(x)= … Read more

Example 1Find the inverse function of the following function (a) f(x) = 4 – 7x,(b) f ( x ) = 2 x + 5 3 Example 2Find the inverse function of the following function (a) f ( x ) = 5 7 x (b) f ( x ) = 2 3 − x Example 3Find … Read more

Inverse  Functions1. Consider the function (f : x maps to  – 2) with domain A = {1, 3, 4, 7}. Then the range of the function is B = {-1, 1, 2, 5}. The arrow diagram representing this function is shown as below.2. If the arrows of (a) are reversed, the arrow diagram in (b) … Read more

Example 1 (substitution Method)A function f is defined by f : x ↦ x + 2  . Find the function g if g f : x ↦ x 2 + 3 x + 5  . [Note : Second function is given, use substitution y = x + 2] Example 2 (Substitution Method)A function f is … Read more

Example 1A function f is defined by f : x ↦ 2 x + 5  . Find the function g if f g : x ↦ 3 x − 8  . [Note : First function f is given] Example 2A function f is defined by f : x ↦ 2 x . Find the function … Read more

Example 1Given f : x ↦ h x + k , g : x ↦ ( x + 1 ) 2 + 4   and f g : x ↦ 2 ( x + 1 ) 2 + 5.   Find (a) the value of g²(2), (b) the value of h and of k. Example … Read more