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1.5 B: Algebra and functions

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Question 172

The light intensity III (in lumens) of a specialized lamp at a distance x x\,x meters is modeled by the function

I(x)=40x+3,x>0,x∈R I(x) = \frac{40}{x + 3}, \quad x > 0, x \in \mathbb{R} I(x)=x+340​,x>0,x∈R

A control system adjusts the distance x x\,x based on a setting s s\,s according to the function

g(s)=52ln⁡s,s>1,s∈R g(s) = \frac{5}{2} \ln s, \quad s > 1, s \in \mathbb{R} g(s)=25​lns,s>1,s∈R
a.

Determine, in simplest form, the value of the composite function Ig(e2)Ig(e^2)Ig(e2).

[2]
b.

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

[3]
c.

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

I−1(x)=I(x) I^{-1}(x) = I(x) I−1(x)=I(x)
[4]
Markscheme

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 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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