Skip to content

Course home

3.1 Algebra and functions (A-level only)

3.1 Algebra and functions (A-level only)

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216
Question 201

The functions fff and ggg are defined by

f(x)=3+4ln⁡x,x>0 f(x) = 3 + 4\ln x, \quad x > 0 f(x)=3+4lnx,x>0 g(x)=8x−42x+1,x>12 g(x) = \frac{8x - 4}{2x + 1}, \quad x > \frac{1}{2} g(x)=2x+18x−4​,x>21​
a.

Find f−1(15)f^{-1}(15)f−1(15).

[2]
b.

Use differentiation to prove that ggg is an increasing function.

[3]
c.

Find g−1(x)g^{-1}(x)g−1(x).

[3]
d.

Find the range of the composite function fgfgfg.

[3]
Markscheme

3.1 Algebra and functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.1 Algebra and functions (A-level only)

281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank