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3.2.3 Algebra and Functions (A-level only)

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Question 49

The output power level PPP of a specific amplifier, in decibels, depends on the signal strength sss according to the function:

P(s)=5+2ln⁡s,s>0 P(s) = 5 + 2\ln s, \quad s > 0 P(s)=5+2lns,s>0

The signal strength SSS produced by a sensor over time ttt (in seconds) is given by:

S(t)=12t−182t+3,t>1.5 S(t) = \frac{12t - 18}{2t + 3}, \quad t > 1.5 S(t)=2t+312t−18​,t>1.5
a.

Determine the value of P−1(9)P^{-1}(9)P−1(9).

[2]
b.

Use differentiation to show that SSS is an increasing function for all t>1.5t > 1.5t>1.5.

[3]
c.

Find an expression for the inverse function S−1(x)S^{-1}(x)S−1(x).

[3]
d.

Determine the range of the composite function PSPSPS.

[3]

3.2.3 Algebra and Functions (A-level only) Questions

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