Question

Select each pair of functions that are inverses of each other.

a) y=2x+3 and 1/2x-3
b) y=x^2 and y=√x
c) y=3x+ 2 and y=1/3x-2/3
d) y=1/x and y=x

Answer 1

In order to determine if functions are inverses, substitute one into the other and check if the result is the original value. Analyzing each pair of functions, we can determine which are inverses.

Step-by-step explanation:

In order for two functions to be inverses of each other, when you substitute one function into the other, you should end up with the original value. Let's analyze each pair of functions:

a) y=2x+3 and 1/2x-3:

Substituting y=2x+3 into 1/2x-3:

1/2x-3 = 2x + 3

1/2x = 2x + 6

2x(1/2x) = 2x(2x + 6)

1 = 4x² + 12x

4x² + 12x - 1 = 0

The resulting equation does not match the original equation, so these functions are not inverses of each other. Therefore, option a) is incorrect.

Now you can continue the same analysis with options b), c), and d) to determine the correct pairs of inverse functions.