Maths Worksheet - Functions, Inverses And Logarithms (answers)

SAEP Matric Success – Zisukhanyo Maths Worksheet Tuesday 24th February 2009 Functions, Inverses and Logarithms - ANSWERS 1. Classroom Mathematics, Exercise 2.1, Q2 a) one-to-one b) one-to-one c) one-to-one d) not one-to-one e) one-to-one f) not one-to-one 2. Study & Master (Standard Grade), Test 3a, Q1-4 a) 4 b) (2,0) and (0,-4) c) 2 x + y = 3 d) x = 2 y +1 3. Study & Master (Higher Grade), Test 1b, Q1 a) 0 or 5/6 or -1/2 b) 4/3 or 0 c) 1/3 or -1 or 0 or -2/3 d) 2/3 or -1 e) -2/3 or 5 f) 7 or 2. Final solution x = 2. g) 1/2 or -1 or -1,28 or 0,78 h) 10/3 or 5/3. Final solution 5/3 4. Study & Master (Higher Grade), Test 1b, Q4 x=

5b ± − 8a 2 b + 25b 2 4a

5. Study & Master (Higher Grade), Test 1b, Q5 a) 2 or 3 b) 2 or -1 6. Study & Master (Higher Grade), Test 5a, Q1.5 7. Classroom Mathematics, Exercise 2.3, Q2 (a-d) a) f-1(x) = 1/3x domain f-1(x) = (-∞,∞)range f-1(x) = ( -∞,∞) -1 b) f (x) = -x domain f-1(x) = (-∞,∞)range f-1(x) = ( -∞,∞) c) f-1(x) = x + 3 domain f-1(x) = (-∞,∞)range f-1(x) = ( -∞,∞) -1 d) f (x) = 2x + 2 domain f-1(x) = (-∞,∞)range f-1(x) = ( -∞,∞) 8. Study & Master (Higher Grade), Test 5a, Q3 a) domain = {x : x ≥ 0 , x ε R} range = {y : y ≤ 0 , y ε R} b) g : x → x2 and x ≤ 0 c) g-1 : y = -√x therefore y ≤ 0. Thus for g : x ≤ 0 9. Classroom Mathematics, Exercise 5.4, Q1 (a-d) a) -34 b) 13 c) -8 d) -11/2 10. Classroom Mathematics, Exercise 5.4, Q6 a=2,b=3