Identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}

Solution:

f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)} [Given]

f (x) = 1/2 x - 1

It can be written as

y = 1/2x - 1

x = 1/2 y - 1 (inverse function)

By adding 1 on both sides

x + 1 = 1/2 y - 1 + 1

Multiply 2 on both sides

2 (x + 1) = 2 (1/2 y)

2x + 2 = y

2x + 2 = f^-1(x)

2x + 2 = g (x)

We get

g (x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

g (x) = 2x + 2

Therefore, the inverse g (x) is {(3, 8), (1, 4), (-1, 0), (-3, -4)}.

Identify the inverse g(x) of the given relation f(x). f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}

Summary:

The inverse g(x) of the given relation f(x), f(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)} is {(3, 8), (1, 4), (-1, 0), (-3, -4)}.