Composite functions Problem set B Answers

1. (a) \(7 - 2 x^{2}\)
2. (b) \(4 x^{2} - 28 x + 49\)

1. (a) \(9 x^{2} + 12 x - 1\)
2. (b) 14

1. (a) \(x \geq 1\)
2. (b) \(x > 2\)

1. (a) 7
2. (b) a = 2 or 6

1. (a) \(f(x)=x^5\), \(g(x)=2x-9\)
2. (b) \(f(x)=\sqrt{x}\), \(g(x)=6-x\)
3. (c) \(f(x)=\ln x\), \(g(x)=x^2+4\)

\(x=\pm3.87\)

1. (a) \(0.9 p + 4.5\)
2. (b) \(0.9 p + 4.05\)
3. (c) £58.50 and £58.05. Fee added first, then the voucher, is cheaper.

1. (a) \(A=\pi(2t+1.5)^2\)
2. (b) 177 m²

x = 1, 3, 5 or 7

1. (a) \(\frac{1}{3 x - 4}\)
2. (b) \(x \neq \frac{4}{3}\)

k = 3

\(x=-1.58\) or \(x=-0.423\)