g(x) = x2, for the domain x ≤ 0. State the range of g(x) for this domain.
(Total for Question 7 is 1 mark)
8
f(x) = 3x - 1 and g(x) = x + 4. Find fg(x), giving your answer in the form ax + b.
(Total for Question 8 is 2 marks)
9
f(x) = 3x - 1 and g(x) = x + 4. Find gf(x), giving your answer in the form ax + b.
(Total for Question 9 is 2 marks)
10
f(x) = (x + 5)/2. Find f-1(x).
(Total for Question 10 is 2 marks)
11
f(x) = 2x - 7 and g(x) = x2 + 3. Find fg(x).
(Total for Question 11 is 2 marks)
12
f(x) = x2 - 5, for the domain x ≥ 0. Find f-1(x), stating its domain.
(Total for Question 12 is 2 marks)
13
f(x) = (2x - 1)/3. Find f-1(x).
(Total for Question 13 is 2 marks)
14
f(x) = 2x + 1 and g(x) = x2 - 4.
(a)Find fg(x), giving your answer in the form ax2 + b.(1)
(b)Find gf(x), giving your answer in the form ax2 + bx + c.(1)
(c)State, with a reason, whether fg(x) = gf(x) for all values of x.(1)
(Total for Question 14 is 3 marks)
15
f(x) = (3x + 2)/(x - 1), where x ≠ 1. Find f-1(x), stating the value which x cannot take.
(Total for Question 15 is 3 marks)
16
A parking garage charges a fee, in pounds sterling, for a stay of t hours given by C(t) = 1.5t + 2. A stay of m minutes converts to hours using the function h(m) = m/60.
(a)Find an expression for C(h(m)), the fee in terms of the stay m in minutes.(2)
(b)Use your expression to find the cost of a 120-minute stay.(1)
(Total for Question 16 is 3 marks)
17
f(x) = (x + 6)/(x - 1), where x ≠ 1. Show that f is a self-inverse function.
(Total for Question 17 is 3 marks)
18
f(x) = ax + b, where a and b are constants. Given that f(2) = 9 and f-1(1) = -2, find the values of a and b.