Question

Find the equation representing the inverse of the given function. (Type or insert picture of your work and final answer.)

a) y = (x - 12)/7
b) y = (x/7) - 12
c) y = (1/7)(x - 12)
d) y = (1/7)x + 12

Answer 1

To find the inverse of the given functions, the variables x and y are swapped, and then the resulting equation is solved for y. The inverse functions for the given problems are y = 7x + 12, y = 7x + 84, y = 7x + 12, and y = 7x - 84 respectively.

Step-by-step explanation:

To find the inverse of a given function, we essentially switch the roles of the variable x and y and then solve the resulting equation for y. This process involves a few steps for each function:

1. Swap x and y in the original equation.
2. Solve the new equation for y.
3. The new equation, now solved for y, is the inverse of the original function.

a) To find the inverse for y = (x - 12)/7:

1. Swap x and y to get x = (y - 12)/7.
2. Multiply both sides by 7 to get 7x = y - 12.
3. Add 12 to both sides to get 7x + 12 = y.
4. The inverse function is y = 7x + 12.

b) To find the inverse for y = (x/7) - 12:

1. Swap x and y to get x = (y/7) - 12.
2. Add 12 to both sides to get x + 12 = y/7.
3. Multiply both sides by 7 to obtain 7x + 84 = y.
4. The inverse function is y = 7x + 84.

c) To find the inverse for y = (1/7)(x - 12):

1. Swap x and y to get x = (1/7)(y - 12).
2. Multiply both sides by 7 to get 7x = y - 12.
3. Add 12 to both sides to obtain 7x + 12 = y.
4. The inverse function is y = 7x + 12.

d) To find the inverse for y = (1/7)x + 12:

1. Swap x and y to get x = (1/7)y + 12.
2. Subtract 12 from both sides to obtain x - 12 = (1/7)y.
3. Multiply both sides by 7 to get 7x - 84 = y.
4. The inverse function is y = 7x - 84.