Assignment

2020 SAJC JC1 H2 Mathematics Assignment 5: Functions Name: ___________________________ Marks: /15 Class: 20___________ Time: 30 min 1. [NYJC/2017/Prelim/P1/Q7] The functions f and g are defined by f : x e - x 2 , x ∈ , x < 0, g : x x 1 1 + 3 , x ∈ , x ≠ - 3. (i) Show that g- 1 exists, and define g- 1 in a similar form. [3] (ii) State the solution set for gg - 1 ( )x = x [1] (iii)Explain why fg- 1 does not exist. [1] Let the function h be defined by h: x g( x ), x ∈ , x < k . Where k is a real constant. (iv) Given that fh- 1 exists, state the maximum value of k. [1] (v) For the value of k found in (iv), (a) find the exact range of fh- 1 , [2] (b) solve h( x ) = h - 1 ( x ). [2] 2. [HCI/2017/Prelim/P1/Q1(modified)] The floor function, denoted by x│ ⌊ │ ⌋ , is the greatest integer less than or equal to x. For example, │ ⌊ - 2.1 │ ⌋ = - 3 and │ ⌊ 3.5 │ ⌋ = 3 . The function f is defined by f( x ) = ⎧ ⎨ ⎩ 0 x for for , , │ ⌊ │ ⌋ x ∈ - 1 ≤ x < 2, x ∈ 2 ≤ x < 3. It is given that f( x ) = f( x + 4) . (i) Find the values of f( - 1.2) and f(3.6) [2] (ii) Sketch the graph of y = f ( x ) for - 2 ≤ x ≤ 4 . [2] (iii) State the range of f. [1]