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1.3 Functions

1.3 Functions

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Question 139

The signal strength fff, measured in decibels (dB), of a satellite transmitter is modeled as a function of the distance x x\,x from the source (in km) by

f(x)=56x+1,x>0,x∈R f(x) = \frac{56}{x + 1}, \quad x > 0, x \in \mathbb{R} f(x)=x+156​,x>0,x∈R

The distance x x\,x is determined by the signal frequency ω\omegaω (in MHz) according to the function

g(ω)=23ln⁡ω,ω>1,ω∈R g(\omega) = \frac{2}{3} \ln \omega, \quad \omega > 1, \omega \in \mathbb{R} g(ω)=32​lnω,ω>1,ω∈R
a.

Find, in simplest form, the value of fg(e9)fg(e^9)fg(e9).

[2]
b.

Find an expression for f−1(x)f^{-1}(x)f−1(x) and state its domain.

[4]
c.

Hence, or otherwise, find all real solutions of the equation

f−1(x)=f(x) f^{-1}(x) = f(x) f−1(x)=f(x)
[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.

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