Skip to content

Course home

Sign up

Functions and Graphs

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242
Question 119

The function f f\,f is defined by f(x)=(x−2)2−4f(x) = (x - 2)^2 - 4f(x)=(x−2)2−4 for x≥kx \geq kx≥k, where k k\,k is a constant.

For parts (b)–(d), take k=2k=2k=2.

a.

Given that f−1(x)f^{-1}(x)f−1(x) exists, state the least possible value of kkk.

[1]
b.

Evaluate ff(5)ff(5)ff(5)

[2]
c.

Solve the equation f(x)=xf(x) = xf(x)=x

[3]
d.

Explain why your answer to part (c) is also the solution to the equation f(x)=f−1(x)f(x) = f^{-1}(x)f(x)=f−1(x)

[1]
Markscheme

Functions and Graphs Questions

  1. A Level
  2. /Maths
  3. /Functions and Graphs

471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank