CAPE Pure Mathematics Unit 1 · 2022 · Paper 2 · Question 2(b)
Solve the equation 6 - \frac{7}{2^{2x}} - \frac{3}{4^{2x}} = 0.
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- 2(a)(i)Let
f(x) = \frac{3x + 1}{x}andg(x) = e^{-2x} + 1. Show thatf^{-1}(x) = \frac{1}{x - 3}.[3 marks] - 2(a)(ii)Hence, or otherwise, write an expression for
(f^{-1} \circ g)(x).[2 marks] - 2(c)The function
f(x) = 2x^3 - px^2 + qx - 10is divisible byx - 1and has a remainder of-6when divided byx + 1. Calculate the values ofpandq.[6 marks] - 2(d)The roots of the equation
2x^3 - x^2 + 3x - 1 = 0are\alpha,\beta, and\gamma. Given that\alpha\beta + \alpha\gamma + \beta\gamma = \frac{3}{2}…[6 marks]
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