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3.1.5 Algebra and functions (A-level only)

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Question 17

The power output, PPP, of a prototype turbine is modeled by the function

P(t)=15(t2+6),t≥0 P(t) = \frac{1}{5}(t^2 + 6), \quad t \ge 0 P(t)=51​(t2+6),t≥0

where ttt is the time in hours since activation.

a.

Find the range of PPP.

[1]
bi.

Find P−1(t)P^{-1}(t)P−1(t).

[2]
bii.

State the range of P−1(t)P^{-1}(t)P−1(t).

[1]
c.

State the geometric transformation which maps the graph of y=P(t)y = P(t)y=P(t) onto the graph of y=P−1(t)y = P^{-1}(t)y=P−1(t).

[1]
d.

Find the coordinates of the points of intersection of the graphs of y=P(t)y = P(t)y=P(t) and y=P−1(t)y = P^{-1}(t)y=P−1(t).

[3]

3.1.5 Algebra and functions (A-level only) Questions

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