2.4 Inverse Functions
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An industrial cooling system's pressure PPP, in bars, is modeled as a function of the coolant flow rate xxx, in litres per second, by:

P(x)=2x2−2.5,x≥0, x∈RP(x) = 2x^2 - 2.5, \quad x \ge 0, \ x \in \mathbb{R}P(x)=2x2−2.5,x≥0, x∈R

a.

State the range of PPP.

A graph showing a coordinate plane with the curve y = P(x). The curve is the right-hand branch of a parabola starting at (0, -2.5) on the y-axis, passing through the x-axis at a positive value, and increasing into the first quadrant. Labels include the origin O and axes x and y.

[1]
b.

Using the diagram provided, sketch the curve with equation y=P−1(x)y = P^{-1}(x)y=P−1(x).

[2]
c.

The curve with equation y=P(x)y = P(x)y=P(x) meets the curve with equation y=P−1(x)y = P^{-1}(x)y=P−1(x) at the point QQQ.

Using algebra and showing your working,

find the exact xxx-coordinate of QQQ.

[5]

2.4 Inverse Functions Questions

Practise Edexcel A Level Maths 2.4 Inverse Functions with exam-style questions for A Level Maths. 41 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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2.4 Inverse Functions Questions

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