HCI Functions Tutorial Q10
HCI Functions Tutorial Q10
Tutorial
An electronically controlled thermostat in a home is programmed to control the temperature automatically throughout a day. The temperature in the house \(T\) (in degrees Celsius) is given in terms of \(t\), the time in hours on \(24\)-hour clock (see graph below).
- Write down a piecewise-defined function \(T\left( t \right)\) that represents the graph.
- Find the temperature of the room at 7.40 am of a day.
- The thermostat is reprogrammed to produce a temperature \(H\) for which \(H\left( t \right)=T\left( t-1 \right)\). How does this change the temperature of the room?
- The thermostat is reprogrammed to produce a temperature \(H\) for which \(H\left( t \right)=T\left( t \right)-1\). How does this change the temperature of the room?
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Answer:(i) \(f^{-1}(x) = \frac{x+3}{x-2}\), \(x > 2\) (ii) \(D_{f^{-1}} = (2, \infty)\) (iii) \(f\mathrm{f}(x) = \frac{7x+3}{x+4}\) (iv) \(x = \frac{3+\sqrt{21}}{2}\)
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