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3.2 Algebra and Functions (A-level only)

3.2 Algebra and Functions (A-level only)

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Question 106

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

3.2 Algebra and Functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.2 Algebra and Functions (A-level only)

216 exam-style questions on WJEC A Level Maths 3.2 Algebra and Functions (A-level only), covering 3.2.1 Algebra and Functions (A-level only), 3.2.2 Algebra and Functions (A-level only), 3.2.3 Algebra and Functions (A-level only), 3.2.4 Algebra and Functions (A-level only), 3.2.5 Algebra and Functions (A-level only), 3.2.6 Algebra and Functions (A-level only), and 3.2 Algebra and Functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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