Inverse functions Problem set A Answers

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

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

x ≥ 4

1. (a) (4.48, 1.5)
2. (b) y = x

(3, 1), (5, 2), (9, 4), (13, 6)

1. (a) 8
2. (b) 4
3. (c) (8, 3)

1. (a) (3.16, 0.5)
2. (b) 0.500. The point \((3.16, 0.5)\) lies on \(y=\log_{10}x\), as the reflection should.

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

1. (a) \(f(x)=(x-4)^2+3\)
2. (b) \(f^{-1}(x)=4+\sqrt{x-3}\)
3. (c) Domain \(x\geq3\); range \(y\geq4\)

1. (a) \(g^{-1}(x)=\frac{5 \left(x - 32\right)}{9}\). It turns a Fahrenheit temperature into Celsius.
2. (b) 35 °C

1. (a) \(f(f^{-1}(x))=x + 14.4\), not x. It is not the inverse.
2. (b) \(f^{-1}(x)=25 x - 375\)

1. (a) 38
2. (b) 4. Four tickets cost £50.
3. (c) (62, 5)

1. (a) (31, 50)
2. (b) 31 miles is 50 km. \(f^{-1}\) turns miles into kilometres.

1. (a) \(f^{-1}(x)=\frac{x + 4}{x}\)
2. (b) 1.5

x ≥ 2

1. (a) (4, 4)
2. (b) (4, 4). A point on the mirror line is its own reflection.

1. (a) \(f^{-1}(x)=e^{(x-2)/2}\)
2. (b) \(x=0.464\) or \(x=5.36\)