Skip to content

Course home

1.3 Functions

1.3 Functions

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148
Question 130

The signal transfer function hhh and the power decay profile qqq are defined by

h(x)=5x+4x−2,x∈R,x≠2 h(x) = \frac{5x + 4}{x - 2}, \quad x \in \mathbb{R}, x \neq 2 h(x)=x−25x+4​,x∈R,x=2 q(x)=3−x2,x∈R,x≤0 q(x) = 3 - x^2, \quad x \in \mathbb{R}, x \le 0 q(x)=3−x2,x∈R,x≤0
a.

Solve the equation hq(x)=4hq(x) = 4hq(x)=4.

[3]
b.

Find h−1(x)h^{-1}(x)h−1(x).

[3]
c.

Sketch and label, on the same axes, the curve with equation y=q(x)y = q(x)y=q(x) and the curve with equation y=q−1(x)y = q^{-1}(x)y=q−1(x). Show on your sketch the coordinates of the points where each curve meets or cuts the coordinate axes.

[4]
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