TMJC Term 4 Revision Chapter 3 Functions Questions

Term 4 Revision Topical Quick Check: Functions TMJC 2024 JC1 H2 Mathematics (9758) Term 4 Revision Topical Quick Check Chapter 3 Functions 1 YIJC Promo 9758/2022/Q9 (modified) The function f is defined by 2f : 4 5xx x −− , for x , 2x . (a) Find 1f ( )x− and state the domain of 1f − . [3] (b) On the same diagram, sketch the graphs of f and 1f − . [3] (c) Find the exact solution of the equation 1f ( ) f ( )xx −= . [3] The function g is defined by 2g: 1x x− , for , 1x x . (d) Explain why the composite function fg exists and find the range of fg. [3] 2 HCI Promo 9758/2022/Q6 The function h is defined as follows. ( ) 321h : 6 32 ,8x x x −+ .x (i) Explain why h does not have an inverse. [1] (ii) If the domain of h is restricted to 0, xk state the largest value of k for which the function 1h− exists. [1] Use the domain of h in part (ii) for the rest of this question. (iii) Sketch the graphs of h and 1h− on the same diagram, showing clearly the relationship between the two graphs, and the coordinates of the end points for both graphs. [3] (iv) Deduce the solution(s) of the equation ( ) ( ) 1hhxx −= . [2] (v) The function g is defined as follows. ( )( ) 2 g : ln 3 1 ,xx −+ .x Show that the composite function gh exists and find the exact range of gh. [2]

Term 4 Revision Topical Quick Check: Functions TMJC 2024 3 CJC Promo 9758/2022/Q10(b) Functions g and h are defined by 2 1g : , , 1,1 h : 1 2 , . x x x x x x x − − (i) Explain why the composite function gh does not exist. [2] (ii) Find ( )hg x . [1] (iii) Find the range of ( )hg x . [2] (iv) By using the result in part (ii), or otherwise find ( ) ( ) 1 hg 4 − . [3]