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)?
It would be: {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
Answer:
The function h⁻¹(x) is \(h(x)=\{(-5,3),(-7,5),(-9,6),(-12,10),(-16,12)\}\).
Step-by-step 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 \(h(x)=\{(-5,3),(-7,5),(-9,6),(-12,10),(-16,12)\}\).