Question

Y = x - 1, Inverse of y is y

= X-1
First, switch a and y so that x = y - 1
Second,
solve for y so that y
= x - 1, therefore the inverse of y = x – 1
1. True
2. false

Answer 1

The claim that the inverse of the function y = x - 1 is itself is false. The correct inverse of the function is y = x + 1, found by interchanging x and y and then solving for y.

Step-by-step explanation:

The assertion that the inverse of the function y = x - 1 is itself, meaning y = x - 1, is false. To find the inverse of a function, we typically swap the x and y variables and then solve for y.

Let's find the inverse step-by-step:

1. Begin with the original function: y = x - 1.
2. Swap x and y to get: x = y - 1.
3. Solve for y: y = x + 1.

The correct inverse function is y = x + 1. To confirm that this is the inverse, you can verify that when we put y(x) into y-1(x), and vice versa, it would lead us back to x, fulfilling the property of inverse functions.