1.3.4 Composite functions (A-level only)

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Question 17

A sensor's output voltage $V$ , in volts, is modeled by the function $3\ln p, \, p > 0$ , where $p\,$ is the internal pressure in kilopascals. The pressure is controlled by a mechanical setting $x\,$ such that $p(x)=12x−63x+1\displaystyle p(x) = \frac{12x - 6}{3x + 1}$ for $x > 0.5$ .

a.

Find $V^{-1}(13)$ .

[2]

b.

Use differentiation to prove that $p\,$ is an increasing function for $x > 0.5$ .

[3]

c.

Find $p^{-1}(x)$ .

[3]

d.

Determine the range of the composite function $V p$ .

[3]

1.3.4 Composite functions (A-level only)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Question 17

A sensor's output voltage $V$ , in volts, is modeled by the function $3\ln p, \, p > 0$ , where $p\,$ is the internal pressure in kilopascals. The pressure is controlled by a mechanical setting $x\,$ such that $p(x)=12x−63x+1\displaystyle p(x) = \frac{12x - 6}{3x + 1}$ for $x > 0.5$ .

a.

Find $V^{-1}(13)$ .

[2]

b.

Use differentiation to prove that $p\,$ is an increasing function for $x > 0.5$ .

[3]

c.

Find $p^{-1}(x)$ .

[3]

d.

Determine the range of the composite function $V p$ .

[3]

1.3.4 Composite functions (A-level only)

Question 17

1.3.4 Composite functions (A-level only) Questions

1.3.4 Composite functions (A-level only)

Question 17

1.3.4 Composite functions (A-level only) Questions