Question

Help please

1. Find the inverse function of y = -3x + 8

2. Find the inverse function of y = 3/5x - 12

Answer 1

1. (x-8)/-3=y

2. (5x/3)+20=y

Explanation:

1. switch x and y

x=-3y+8

solve for y

x-8=-3y

(x-8)/-3=y

2. x=3/5y-12

x+12=3/5y

(5x/3)+20=y

Answer 2

Question 1:

For this case we must find the inverse of the following function:

`y = -3x + 8`

To do this we follow the steps below:

We exchange the variables:

`x = -3y + 8`

We clear the value of the variable "y":

`x-8 = -3y\\y = \frac {x-8} {- 3}\\y = \frac {8-x} {3}`

We change y for
`f^(-1)(x):`

`f ^(-1)(x) = \frac {8-x} {3}`

ANswer:

The inverse of the given function is
`f ^ {-1} (x) = \frac {8-x} {3}`

Question 2:

For this case we must find the inverse of the following function:

`y = \frac {3} {5} x-12`

To do this we follow the steps below:

We exchange the variables:

`x = \frac {3} {5} y-12`

We clear the value of the variable "y":

`x + 12 = \frac {3} {5} y\\5 (x + 12) = 3y\\5x + 60 = 3y\\y = \frac {5x} {3} + \frac {60} {3}\\y = \frac {5x} {3} +20`

We change y for
`f^(-1)(x)`:

`f^(-1)(x) = \frac {5x} {3} +20`

ANswer:

The inverse of the given function is:
`f ^ {-1} (x) = \frac {5x} {3} +20`