Skip to content

Course home

Sign up

1.3 Functions

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041
Question 38

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

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank