Question

6-2 inverse relations and functions • practice
date 12-11
period
example 1
for each polygon, find the inverse of the relation. then, graph both the original relation and its inverse.

1. △jkp with vertices at {(-8, 6), (6, -2), (4, -6)}
2. trapezoid qrst with vertices {(8, -1), (-8, -1), (-2, -8), (2, -8)}

examples 2 and 3
find the inverse of each function. then graph the function and its inverse. if necessary, restrict the domain of the inverse so that it is a function.

1. f(x) = x + 2
2. f(x) = -2x + 1
3. f(x) = -\frac{4}{3}x - 8
4. f(x) = 4x

Explanation:

Step1: Swap x and y

Given the function \( f(x) = 4x \), we can write it as \( y = 4x \). To find the inverse, we first swap \( x \) and \( y \), so we get \( x = 4y \).

Step2: Solve for y

Now, we solve the equation \( x = 4y \) for \( y \). We divide both sides of the equation by 4: \( y=\frac{x}{4} \). So the inverse function of \( f(x) = 4x \) is \( f^{-1}(x)=\frac{1}{4}x \).

Answer:

The inverse of the function \( f(x) = 4x \) is \( f^{-1}(x)=\frac{1}{4}x \)