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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 82

A signal processing unit models the gain G G\,G as a function of input voltage v v\,v according to the rule

G(v)=5−3v2v+1,v∈R,v≠−0.5 G(v) = \frac{5 - 3v}{2v + 1}, \quad v \in \mathbb{R}, v \neq -0.5 G(v)=2v+15−3v​,v∈R,v=−0.5

The input voltage v v\,v is determined by the time t t\,t in seconds via the function

V(t)=4−2t,t∈R V(t) = 4 - 2t, \quad t \in \mathbb{R} V(t)=4−2t,t∈R
a.

Evaluate the composite gain GV(−1.5)GV(-1.5)GV(−1.5).

[2]
b.

Obtain an expression for the inverse gain function G−1(x)G^{-1}(x)G−1(x).

[3]
c.

Determine the values of k k\,k that satisfy the equation G(1k)=V(k+1)\displaystyle G\left(\frac{1}{k}\right) = V(k + 1)G(k1​)=V(k+1).

[5]
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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