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1.3 Functions

1.3 Functions

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Question 132

A sensor's output voltage VVV, in volts, is modeled by the function V(p)=7+3ln⁡p, p>0V(p) = 7 + 3\ln p, \, p > 0V(p)=7+3lnp,p>0, where p p\,p is the internal pressure in kilopascals. The pressure is controlled by a mechanical setting x x\,x such that p(x)=12x−63x+1\displaystyle p(x) = \frac{12x - 6}{3x + 1}p(x)=3x+112x−6​ for x>0.5x > 0.5x>0.5.

a.

Find V−1(13)V^{-1}(13)V−1(13).

[2]
b.

Use differentiation to prove that p p\,p is an increasing function for x>0.5x > 0.5x>0.5.

[3]
c.

Find p−1(x)p^{-1}(x)p−1(x).

[3]
d.

Determine the range of the composite function VpVpVp.

[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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