Inverse functions Problem set B Answers

1. (a) \(f^{-1}(x)=\frac{x - 9}{5}\)
2. (b) \(g^{-1}(x)=\frac{7 - 3 x}{4}\)

1. (a) f(g(x)) = x
2. (b) g(f(x)) = x

x ≥ 6

1. (a) (1.10, 3)
2. (b) y = x

(1, 0), (7, 2), (10, 3), (16, 5)

1. (a) 9
2. (b) 3
3. (c) (9, 2)

1. (a) (0.699, 5)
2. (b) 5.00. The point \((0.699, 5)\) lies on \(y=10^x\), as the reflection should.

1. (a) \(f^{-1}(x)=\ln\!\left(\frac{x+3}{4}\right)\), \(x>-3\)
2. (b) \(g^{-1}(x)=e^{(x-5)/2}\), all real x

1. (a) \(f(x)=(x+5)^2+6\)
2. (b) \(f^{-1}(x)=-5+\sqrt{x-6}\)
3. (c) Domain \(x\geq6\); range \(y\geq-5\)

1. (a) \(c^{-1}(x)=\frac{2 x - 5}{3}\). It turns a fare into a distance.
2. (b) 11.7 km

1. (a) \(f(f^{-1}(x))=x - 60\), not x. It is not the inverse.
2. (b) \(f^{-1}(x)=0.4 x - 16\)

1. (a) 15
2. (b) 8. A fare of £19 is for a journey of 8 km.
3. (c) (23, 10)

1. (a) (52, 40)
2. (b) 52 dollars is £40. \(g^{-1}\) turns dollars into pounds.

1. (a) \(f^{-1}(x)=\frac{2 \left(3 - x\right)}{x}\)
2. (b) −1.25

x ≥ 3

1. (a) (5, 5)
2. (b) (5, 5). A point on the mirror line is its own reflection.

1. (a) \(f^{-1}(x)=e^{(x-0.5)/3}\)
2. (b) \(x=1.31\) or \(x=5.74\)