Question

The function h(x) is given below. h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)} Which of the following gives h–1(x)?

Answer 1

It would be: {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}

Answer 2

The function h⁻¹(x) is
`h(x)=\{(-5,3),(-7,5),(-9,6),(-12,10),(-16,12)\}`.

Explanation:

If a function is defined as

`f(x)=\{(x,y):x\in R,y\in R\}`

Then,

`f^(-1)(x)=\{(y,x):x\in R,y\in R\}`

The given function is

`h(x)=\{(3,-5),(5,-7),(6,-9),(10,-12),(12,-16)\}`

Interchange the x and y coordinates of each point to find the h⁻¹(x).

`h(x)=\{(-5,3),(-7,5),(-9,6),(-12,10),(-16,12)\}`

Therefore the function h⁻¹(x) is
`h(x)=\{(-5,3),(-7,5),(-9,6),(-12,10),(-16,12)\}`.