Show that the composite function $E E (v)$ can be written in the form $av+bv+c\displaystyle \frac{av + b}{v + c}$ , where $b,\,$ and $c\,$ are integers to be found.

[3]

cii.

Deduce the range of $E E$ .

[3]

3.2.3 Algebra and Functions (A-level only) Questions

A Level
Maths
3.2.3 Algebra and Functions (A-level only)

A Level
Maths WJEC
Question bank

3.2.3 Algebra and Functions (A-level only)

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Question 48

The cooling efficiency, $E$ , of a high-performance server rack is modelled by the function

\frac{5v - 2}{v - 4}, \quad v > 4

where $v\,$ is the coolant flow rate in litres per minute.

Use differentiation to show that $E\,$ is a decreasing function on its domain.

[3]

Find an expression for $E^{-1}(v)$ and state its domain.

[4]

ci.

Show that the composite function $E E (v)$ can be written in the form $av+bv+c\displaystyle \frac{av + b}{v + c}$ , where $b,\,$ and $c\,$ are integers to be found.

[3]

cii.

Deduce the range of $E E$ .

[3]

3.2.3 Algebra and Functions (A-level only) Questions

A Level
Maths
3.2.3 Algebra and Functions (A-level only)