Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 8
106 practice questions
Topics covered
Practice questions
11–20 of 47 · Normal
Question 11
3 marks · Normal
Answer and see the solution →Let f(x) = 2x + 1 and g(x) = x^2.
Explain how to find the value of the composite function fg(3), and work it out.
Question 12
4 marks · Normal
Answer and see the solution →The function f is defined by f(x) = 4x + 1.
a) Show, by algebraic method, how to find the inverse function f^{-1}(x).
b) Use your result to find f^{-1}(13).
(a)[3 marks]Show, by algebraic method, how to find the inverse function f^{-1}(x).
(b)[1 mark]Use your result to find f^{-1}(13).
Question 13
4 marks · Normal
Answer and see the solution →The following table gives the mapping from numbers in set P to set Q.
Mapping Table P Q 1 −2 2 0 3 2 4 4 For this mapping:
(a)[1 mark]Is this mapping a function? Give a reason.
(b)[2 marks]Write down the domain and range of the mapping.
(c)[1 mark]Is this function one-to-one or many-to-one? Explain.
Question 14
2 marks · Normal
Answer and see the solution →Let f(x) = 2x + 3. State the domain and the range of f when the domain is {−2, 0, 4}.
Question 15
3 marks · Normal
Answer and see the solution →Given f(x) = 2x − 1 and g(x) = x^2. Find the value of gf(4).
Question 16
3 marks · Normal
Answer and see the solution →Given the function k(x) = 3x − 4, explain step by step how to find its inverse, and then write down k^{-1}(x).
Question 17
2 marks · Normal
Answer and see the solution →The graph below shows the curve for .
Graph of \( y = x^2 \) for \( x \) from \( -3 \) to \( 3 \). Question 18
3 marks · Normal
Answer and see the solution →Use a graph to solve the equation for between -3 and 3.
State what two graphs you would draw and explain how their intersection gives the solution.
Question 19
3 marks · Normal
Answer and see the solution →Two graphs are drawn: and .
Explain how you would use these graphs to solve the equations:
a)
b)
Show clear reasoning.
Question 20
4 marks · Normal
Answer and see the solution →The graph below shows the curve for .
Graph of \( y = x^2 - 4x + 2 \) on \( 0 \leq x \leq 5 \) (a)[2 marks]Use the graph to estimate the solutions of for .
(b)[2 marks]By drawing a suitable straight line on the graph, use it to solve the equation for .