Title Topic 2 Part 1 T.pdf ✅

2a. [4 marks] A function is defined by . Find an expression for . f f(x) = , x ∈ R, x ≠ 3x−2 2x−1 1 2 f (x) −1 2b. Given that f(x) can be written in the form f(x) = A + , find the values of the constants and . [2 marks] B 2x−1 A B 2c. Hence [1 mark] , write down ∫ dx. 3x−2 2x−1 5 4 3 2 R
3a. [3 marks] Let . For the polynomial equation , state (i) the sum of the roots; (ii) the product of the roots. p(x) = 2x 5 + x 4 − 26x 3 − 13x 2 + 72x + 36, x ∈ R p(x) = 0 3b. A new polynomial is defined by . [2 marks] Find the sum of the roots of the equation . q(x) = p(x + 4) q(x) = 0 4a. [1 mark] The functions and are defined by and . Show that . f g f(x) = 2x + , x ∈ R π 5 g(x) = 3 sin x + 4, x ∈ R g ∘ f(x) = 3 sin(2x + ) + 4 π 5 ∘
4b. Find the range of g ∘ f. [2 marks] 4c. Given that g ∘ f ( ) = 7, find the next value of , greater than , for which . [2 marks] 3π 20 x 3π 20 g ∘ f(x) = 7 4d. The graph of can be obtained by applying four transformations to the graph of . State [4 marks] what the four transformations represent geometrically and give the order in which they are applied. y = g ∘ f(x) y = sin x 3 R